CHAPTER 6 FLUID MECHANICS YEAR ONE MARK MCQ 6. MCQ 6. Oil flows through a mm diameter horizontal cast iron pipe (friction factor, f. 5) of length 5 m. The volumetric flow rate is. m / s. The head loss (in m) due to friction is (assume g 9.8 m/ s ) (A) 6.8 (B).6 (C) 8. (D).6 The velocity triangles at the inlet and exit of the rotor of a turbomachine are shown. V denotes the absolute velocity of the fluid, W denotes the relative velocity of the fluid and U denotes the blade velocity. Subscripts and refer to inlet and outlet respectively. If V W and V W, then the degree of reaction is (A) (B) (C).5 (D).5 YEAR TWO MARKS MCQ 6. MCQ 6.4 An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is mm at a location where the Reynolds number is. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be (A) 4 (B) (C).5 (D).5 A large tank with a nozzle attached contains three immiscible, inviscide fluids as shown. Assuming that the change in h, handh are negligible, the Published by: NODIA and COMPANY ISBN: 97889765
PAGE 48 FLUID MECHANICS CHAP 6 instantaneous discharge velocity is (A) (C) ρ gh h ρ h c + + ρ h ρ h m (B) gh ( + h+ h) ρh+ ρh+ ρh ρ hh+ ρ hh+ ρ hh gc ρ + ρ + ρ m (D) g ρ h + ρ h + ρ h YEAR ONE MARK MCQ 6.5 A streamline and an equipotential line in a flow field (A) are parallel to each other (B) are perpendicular to each other (C) intersect at an acute angle (D) are identical YEAR TWO MARKS MCQ 6.6 Figure shows the schematic for the measurement of velocity of air (density. kg/ m ) through a constant area duct using a pitot tube and a water tube manometer. The differential head of water (density kg/ m ) in the two columns of the manometer is mm. Take acceleration due to gravity as 9.8 m/ s. The velocity of air in m/s is (A) 6.4 (B) 9. (C).8 (D) 5.6 MCQ 6.7 A pump handing a liquid raises its pressure from bar to bar. Take the Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 49 density of the liquid as 99 kg/ m. The isentropic specific work done by the pump in kj/kg is (A). (B). (C).5 (D).9 YEAR ONE MARK MCQ 6.8 MCQ 6.9 MCQ 6. MCQ 6. For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE? (A) Metacenter should be below centre of gravity. (B) Metacenter should be above centre of gravity. (C) Metacenter and centre of gravity must lie on the same horizontal line. (D) Metacenter and centre of gravity must lie on the same vertical line. The maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is 6ms. The mean velocity (in ms ) of the flow is (A) (B) (C) 4 (D) 5 A phenomenon is modeled using n dimensional variables with k primary dimensions. The number of non-dimensional variables is (A) k (B) n (C) n k (D) n+ k A hydraulic turbine develops kw power for a head of 4 m. If the head is reduced to m, the power developed (in kw) is (A) 77 (B) 54 (C) 5 (D) 77 YEAR TWO MARKS MCQ 6. Velocity vector of a flow field is given as V xyi x zj. The vorticity vector at (,,) is (A) 4i j (B) 4i k (C) i 4j (D) i 4k MCQ 6. A smooth pipe of diameter mm carries water. The pressure in the pipe at section S (elevation : m) is 5 kpa. At section S (elevation : m) the pressure is kpa and velocity is ms. Density of water is kgm and acceleration due to gravity is 9.8 ms. Which of the following is TRUE Published by: NODIA and COMPANY ISBN: 97889765
PAGE 5 FLUID MECHANICS CHAP 6 (A) flow is from S to S and head loss is.5 m (B) flow is from S to S and head loss is.5 m (C) flow is from S to S and head loss is.6 m (D) flow is from S to S and head loss is.6 m MCQ 6.4 Match the following P. Compressible flow U. Reynolds number Q. Free surface flow V. Nusselt number R. Boundary layer flow W. Weber number S. Pipe flow X. Froude number T. Heat convection Y. Mach number Z. Skin friction coefficient (A) P-U; Q-X; R-V; S-Z; T-W (B) P-W; Q-X; R-Z; S-U; T-V (C) P-Y; Q-W; R-Z; S-U; T-X (D) P-Y; Q-W; R-Z; S-U; T-V YEAR 9 TWO MARKS MCQ 6.5 MCQ 6.6 Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from cm to cm. The pressure in the cm pipe just upstream of the reducer is 5 kpa. The fluid has a vapour pressure of 5 kpa and a specific weight of 5 kn/ m. Neglecting frictional effects, the maximum discharge ( in m / s) that can pass through the reducer without causing cavitation is (A).5 (B).6 (C).7 (D).8 You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices, expressed in terms of the two dimensional velocity fields in the xy-plane, are made available. P : u y, v x Q : u xy, v R : u x, v y Which flow(s) should be recommended when the application requires the flow to be incompressible and irrotational? (A) P and R (B) Q (C) Q and R (D) R Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 5 MCQ 6.7 MCQ 6.8 Water at 5c C is flowing through a. km long. G.I. pipe of mm diameter at the rate of.7 m / s. If value of Darcy friction factor for this pipe is. and density of water is kg/ m, the pumping power (in kw) required to maintain the flow is (A).8 (B) 7.4 (C).5 (D) 4. The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression ur () R dp r 4μbdx lc R m dp Where is a constant. The average velocity of fluid in the pipe is dx (A) (C) R dp 8μbdx l (B) R dp 4μbdx l R dp μbdx l (D) R dp μ bdx l YEAR 8 ONE MARK MCQ 6.9 For the continuity equation given by d : V to be valid, where V is the velocity vector, which one of the following is a necessary condition? (A) steady flow (B) irrotational flow (C) inviscid flow (D) incompressible flow YEAR 8 TWO MARKS MCQ 6. Water, having a density of kg/ m, issues from a nozzle with a velocity of m/ s and the jet strikes a bucket mounted on a Pelton wheel. The wheel rotates at rad/ s. The mean diameter of the wheel is m. The jet is split into two equal streams by the bucket, such that each stream is deflected by c as shown in the figure. Friction in the bucket may be neglected. Magnitude of the torque exerted by the water on the wheel, per unit mass flow rate of the incoming jet, is Published by: NODIA and COMPANY ISBN: 97889765
PAGE 5 FLUID MECHANICS CHAP 6 (A) (N-m)/(kg/s) (C).5 (N-m)/(kg/s) (B).5 (N-m)/(kg/s) (D).75 (N-m)/(kg/s) Common Data For Q. and Q. The gap between a moving circular plate and a stationary surface is being continuously reduced, as the circular plate comes down at a uniform speed V towards the stationary bottom surface, as shown in the figure. In the process, the fluid contained between the two plates flows out radially. The fluid is assumed to be incompressible and inviscid. MCQ 6. The radial velocity V r at any radius r, when the gap width is h, is (A) V Vr r (B) V Vr r h h (C) V Vh r (D) V r MCQ 6. The radial component of the fluid acceleration at r R is (A) V R (B) V R 4h 4h (C) V R h r (D) V h R Vh r Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 5 YEAR 7 ONE MARK MCQ 6. MCQ 6.4 MCQ 6.5 Consider an incompressible laminar boundary layer flow over a flat plate of length L, aligned with the direction of an incoming uniform free stream. If F is the ratio of the drag force on the front half of the plate to the drag force on the rear half, then (A) F < / (B) F / (C) F (D) F > In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by v u( + x/ L), where x is the distance along the axis of the nozzle from its inlet plane and L is the length of the nozzle. The time required for a fluid particle on the axis to travel from the inlet to the exit plane of the nozzle is (A) L (B) L ln 4 u u (C) L (D) L 4u 5. u Consider steady laminar incompressible anti-symmetric fully developed viscous flow through a straight circular pipe of constant cross-sectional area at a Reynolds number of 5. The ratio of inertia force to viscous force on a fluid particle is (A) 5 (B) /5 (C) (D) YEAR 7 TWO MARKS MCQ 6.6 The inlet angle of runner blades of a Francis turbine is 9c. The blades are so shaped that the tangential component of velocity at blade outlet is zero. The flow velocity remains constant throughout the blade passage and is equal to half of the blade velocity at runner inlet. The blade efficiency of the runner is (A) 5% (B) 5% (C) 8% (D) 89% MCQ 6.7 A model of a hydraulic turbine is tested at a head of 4 / th of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine. If N is the RPM of the full scale turbine, the RPM of the model will be (A) N/ 4 (B) N/ (C) N (D) N Published by: NODIA and COMPANY ISBN: 97889765
PAGE 54 FLUID MECHANICS CHAP 6 MCQ 6.8 MCQ 6.9 Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stress is zero at all points in the flow. Q: Vorticity is zero at all points in the flow. R: Velocity is directly proportional to the radius from the center of the vortex. S: Total mechanical energy per unit mass is constant in the entire flow field. (A) P and Q (B) R and S (C) P and R (D) P and S Match List-I with List-II and select the correct answer using the codes given below the lists : List-I List-II P. Centrifugal compressor. Axial flow Q. Centrifugal pump. Surging R. Pelton wheel. Priming S. Kaplan turbine 4. Pure impulse Codes : P Q R S (A) 4 (B) 4 (C) 4 (D) 4 Common Data For Q. and Q. : Consider a steady incompressible flow through a channel as shown below. Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 55 The velocity profile is uniform with a value of U at the inlet section A. The velocity profile at section B downstream is Z ] V y m, # y # δ δ ] u [ Vm, δ # y # H δ V H ] y m, H δ # y # H \ δ MCQ 6. The ratio Vm / U is (A) (B) (/ δ H) (C) (D) (/ δ H) + (/ δ H) p p MCQ 6. The ratio A B (where p A and p B are the pressures at section A and B ) ρu respectively, and ρ is the density of the fluid) is (A) (B) 8 ^δ/ H hb [ ( / H)] δ (C) (D) 6 ( δ/ H) @ + (/ δ H) YEAR 6 ONE MARK MCQ 6. For a Newtonian fluid (A) Shear stress is proportional to shear strain (B) Rate of shear stress is proportional to shear strain (C) Shear stress is proportional to rate of shear strain (D) Rate of shear stress is proportional to rate of shear strain MCQ 6. In a two-dimensional velocity field with velocities u and v along the x and y directions respectively, the convective acceleration along the x -direction is given by (A) u v + v u (B) u u + v v x y x y (C) u u + v u (D) v u + u u x y x y MCQ 6.4 In a Pelton wheel, the bucket peripheral speed is m/ s, the water jet velocity is 5 m/ s and volumetric flow rate of the jet is. m / s. If the jet deflection angle is c and the flow is ideal, the power developed is (A) 7.5 kw (B) 5. kw (C).5 kw (D) 7.5 kw Published by: NODIA and COMPANY ISBN: 97889765
PAGE 56 FLUID MECHANICS CHAP 6 YEAR 6 TWO MARKS MCQ 6.5 MCQ 6.6 MCQ 6.7 A two-dimensional flow field has velocities along the x and y directions given by u x t and v xyt respectively, where t is time. The equation of stream line is (A) x y constant (B) xy constant (C) xy constant (D) not possible to determine The velocity profile in fully developed laminar flow in a pipe of diameter D is given by u u( 4 r / D ), where r is the radial distance from the center. If the viscosity of the fluid is μ, the pressure drop across a length L of the pipe is μul 4μuL (A) (B) D D 8μuL 6μuL (C) (D) D D A siphon draws water from a reservoir and discharge it out at atmospheric pressure. Assuming ideal fluid and the reservoir is large, the velocity at point P in the siphon tube is (A) gh (B) gh (C) gh ( h) (D) gh ( + h) MCQ 6.8 A large hydraulic turbine is to generate kw at rpm under a head of 4 m. For initial testing, a : 4 scale model of the turbine operates under a head of m. The power generated by the model (in kw) will be (A).4 (B) 4.68 (C) 9.8 (D) 8.75 MCQ 6.9 A horizontal-shaft centrifugal pump lifts water at 65c C. The suction nozzle is one meter below pump center line. The pressure at this point equals kpa gauge and velocity is m/s. Steam tables show saturation pressure at 65c C is 5 kpa, and specific volume of the saturated liquid is. m/kg. The pump Net Positive Suction Head (NPSH) in meters is Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 57 (A) 4 (B) 6 (C) 8 (D) Common Data For Q. 4 and Q.4 A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at U m/ s. The thickness of the boundary layer at section r s is mm, the breadth of the plate is m (into the paper) and the density of the gas ρ. kg/m. Assume that the boundary layer is thin, twodimensional, and follows a linear velocity distribution, u U(/) y δ, at the section r-s, where y is the height from plate. MCQ 6.4 The mass flow rate (in kg/s) across the section q r is (A) zero (B).5 (C). (D).5 MCQ 6.4 The integrated drag force (in N) on the plate, between p-s, is (A).67 (B). (C).7 (D) zero YEAR 5 ONE MARK MCQ 6.4 The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively. Then u/ x is equal to (A) v (B) v x x (C) v (D) v y y Published by: NODIA and COMPANY ISBN: 97889765
PAGE 58 FLUID MECHANICS CHAP 6 YEAR 5 TWO MARKS MCQ 6.4 MCQ 6.44 A venturimeter of mm throat diameter is used to measure the velocity of water in a horizontal pipe of 4 mm diameter. If the pressure difference between the pipe and throat sections is found to be kpa then, neglecting frictional losses, the flow velocity is (A). m/s (B). m/s (C).4 m/s (D). m/s A U-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two locations A and B in a conical section through which an incompressible fluid flows. At a particular flow rate, the mercury column appears as shown in the figure. The density of mercury is 6 kg/m and g 9.8 m/ s. Which of the following is correct? MCQ 6.45 (A) Flow direction is A to B and p kpa (B) Flow direction is B to A and pa pb.4 kpa (C) Flow direction is A to B and pb pa kpa (D) Flow direction is B to A and p p.4 kpa Published by: NODIA and COMPANY ISBN: 97889765 p A B A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of m from the centre of the whirlpool. The whirlpool can be described by the following velocity distribution: V 6 r b # π r l m/s and V # θ m/s π r Where r (in metres) is the distance from the centre of the whirlpool. What will be the distance of the leaf from the centre when it has moved through half a revolution? (A) 48 m (B) 64 m (C) m (D) 4 m B A
CHAP 6 FLUID MECHANICS PAGE 59 YEAR 4 ONE MARK 7 MCQ 6.46 An incompressible fluid (kinematic viscosity, 7.4 # m /s, specific gravity,.88) is held between two parallel plates. If the top plate is moved with a velocity of.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of.5 mm between these plates; the shear stress in Pascals on the surfaces of top plate is (A).65 # (B).65 (C) 6.5 (D).65 # MCQ 6.47 A fluid flow is represented by the velocity field V axi+ ayj, where a is a constant. The equation of stream line passing through a point (, ) is (A) x y (B) x+ y (C) x y (D) x+ y YEAR 4 TWO MARKS MCQ 6.48 The following data about the flow of liquid was observed in a continuous chemical process plant : Flow rate (litres / sec) 7.5 to 7.7 7.7 to 7.9 7.9 to 8. 8. to 8. 8. to 8.5 Frequency 5 5 7 8.5 to 8.7 Mean flow rate of the liquid is (A) 8. litres/sec (C) 8.6 litres/sec (B) 8.6 litres/sec (D) 8.6 litres/sec MCQ 6.49 MCQ 6.5 For a fluid flow through a divergent pipe of length L having inlet and outlet radii of R and R respectively and a constant flow rate of Q, assuming the velocity to be axial and uniform at any cross-section, the acceleration at the exit is Q( R R) Q ( R R) (A) (B) πlr πlr (C) Q ( R R) π LR 5 (D) Q ( R R) π LR A closed cylinder having a radius R and height H is filled with oil of density ρ. If the cylinder is rotated about its axis at an angular velocity of ω, then thrust at the bottom of the cylinder is ρω R (A) πr ρ gh (B) πr 4 (C) πr ( ρω R + ρgh) (D) πr 5 ρω R c 4 + ρgh m Published by: NODIA and COMPANY ISBN: 97889765
PAGE 6 FLUID MECHANICS CHAP 6 MCQ 6.5 For air flow over a flat plate, velocity ( U ) and boundary layer thickness ( δ ) can be expressed respectively, as U U y y δ a δ k ; δ 464x. Re x If the free stream velocity is m/s, and air has kinematic viscosity of 5.5 # m /s and density of. kg/m, the wall shear stress at x m, is (A).6 # N/m (B) 4.6 # N/m (C) 4.6 # N/m (D).8 # N/m MCQ 6.5 MCQ 6.5 A centrifugal pump is required to pump water to an open water tank situated 4km away from the location of the pump through a pipe of diameter. m having Darcy s friction factor of.. The average speed of water in the pipe is m/ s. If it is to maintain a constant head of 5m in the tank, neglecting other minor losses, then absolute discharge pressure at the pump exit is (A).449 bar (B) 5.5 bar (C) 44.9 bar (D) 55. bar The pressure gauges G and G installed on the system show pressure of p G 5. bar and p G. bar. The value of unknown pressure p is (A). bar (C) 5. bar (B). bar (D) 7. bar MCQ 6.54 At a hydro electric power plant site, available head and flow rate are 4.5 m and. m / s respectively. If the turbine to be installed is required to run at 4. revolution per second (rps) with an overall efficiency of 9%, the suitable type of turbine for this site is (A) Francis (B) Kaplan (C) Pelton (D) Propeller Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 6 MCQ 6.55 Match List-I with List-II and select the correct answer using the codes given below the lists : List-I List-II P. Reciprocating pump. Plant with power output below kw Q. Axial flow pump. Plant with power output between kw to MW R. Microhydel plant. Positive displacement S. Backward curved vanes 4. Draft tube 5. High flow rate, low pressure ratio 6. Centrifugal pump impeller Codes : P Q R S (A) 5 6 (B) 5 6 (C) 5 6 (D) 4 5 6 YEAR ONE MARK MCQ 6.56 A cylindrical body of cross-sectional area A, height H and density ρ s, is immersed to a depth h in a liquid of density ρ, and tied to the bottom with a string. The tension in the string is (A) ρ gha (B) ( ρ ρ)gha (C) ( ρ ρ s )gha (D) ( ρh ρ s H) ga s YEAR TWO MARKS MCQ 6.57 A water container is kept on a weighing balance. Water from a tap is falling vertically into the container with a volume flow rate of Q; the velocity of the water when it hits the water surface is U. At a particular instant of time Published by: NODIA and COMPANY ISBN: 97889765
PAGE 6 FLUID MECHANICS CHAP 6 the total mass of the container and water is m. The force registered by the weighing balance at this instant of time is (A) mg + ρqu (B) mg + ρqu (C) mg + ρqu / (D) ρqu / MCQ 6.58 Air flows through a venturi and into atmosphere. Air density is ρ ; atmospheric pressure is p a ; throat diameter is D t ; exit diameter is D and exit velocity is U. The throat is connected to a cylinder containing a frictionless piston attached to a spring. The spring constant is k. The bottom surface of the piston is exposed to atmosphere. Due to the flow, the piston moves by distance x. Assuming incompressible frictionless flow, x is MCQ 6.59 (A) ( ρu / k) π D s (B) ( ρu /8 k) D c D (C) ( U / k) D ρ c πds D m (D) ( ρu /8 k) D c D t t 4 4 t mπd s mπd A centrifugal pump running at 5 rpm and at its maximum efficiency is delivering a head of m at a flow rate of 6 litres per minute. If the rpm is changed to, then the head H in metres and flow rate Q in litres per minute at maximum efficiency are estimated to be (A) H 6, Q (B) H, Q (C) H 6, Q 48 (D) H, Q s MCQ 6.6 Match List-I with the List-II and select the correct answer using the codes given below the lists : List-I List-II P Curtis. Reaction steam turbine Q Rateau. Gas turbine R Kaplan. Velocity compounding S Francis 4. Pressure compounding 5. Impulse water turbine 6. Axial turbine Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 6 Codes : P Q R S (A) 6 (B) 5 7 (C) 5 (D) 4 7 6 7. Mixed flow turbine 8. Centrifugal pump MCQ 6.6 MCQ 6.6 Assuming ideal flow, the force F in newtons required on the plunger to push out the water is (A) (B).4 (C). (D).5 Neglect losses in the cylinder and assume fully developed laminar viscous flow throughout the needle; the Darcy friction factor is 64/Re. Where Re is the Reynolds number. Given that the viscosity of water is. # kg/s-m, the force F in newtons required on the plunger is (A). (B).6 (C). (D) 4.4 YEAR ONE MARK MCQ 6.6 MCQ 6.64 If there are m physical quantities and n fundamental dimensions in a particular process, the number of non-dimentional parameters is (A) m+ n (B) m# n (C) m n (D) mn / If x is the distance measured from the leading edge of a flat plate, the laminar boundary layer thickness varies as (A) (B) x 45 / x (C) x (D) x / MCQ 6.65 Flow separation in flow past a solid object is caused by (A) a reduction of pressure to vapour pressure (B) a negative pressure gradient (C) a positive pressure gradient (D) the boundary layer thickness reducing to zero Published by: NODIA and COMPANY ISBN: 97889765
PAGE 64 FLUID MECHANICS CHAP 6 MCQ 6.66 The value of Biot number is very small (less than.) when (A) the convective resistance of the fluid is negligible (B) the conductive resistance of the fluid is negligible (C) the conductive resistance of the solid is negligible (D) None of the above YEAR TWO MARKS MCQ 6.67 The properties of mercury at K are; density 59 kg/ m, specific heat at constant pressure.9 kj/ kg K, dynamic viscosity.5 # Nsm / and thermal conductivity 8.54 W/ m K. The Prandtl number of the mercury at K is (A).48 (B).48 (C) 4.8 (D) 48 YEAR ONE MARK MCQ 6.68 MCQ 6.69 MCQ 6.7 The SI unit of kinematic viscosity (υ) is (A) m / s (B) kg/ m s (C) m/ s (D) m / s A static fluid can have (A) non-zero normal and shear stress (B) negative normal stress and zero shear stress (C) positive normal stress and zero shear stress (D) zero normal stress and non-zero shear stress Lumped heat transfer analysis of a solid object suddenly exposed to a fluid medium at a different temperature is valid when (A) Biot number <. (B) Biot number >. (C) Fourier number <. (D) Fourier number >. YEAR TWO MARKS MCQ 6.7 The horizontal and vertical hydrostatic forces F x and F y on the semi-circular gate, having a width w into the plane of figure, are Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 65 (A) F (B) F (C) F (D) F x x x x ρghrw and Fy ρghrw and F y ρghrw and F ρgwr / ρghrw and F πρgwr / y y MCQ 6.7 The two-dimensional flow with velocity v ( x+ y+ ) i+ (4 y) j is (A) compressible and irrotational (B) compressible and not irrotational (C) incompressible and irrotational (D) incompressible and not irrotational MCQ 6.7 Water (Prandtl number 6) flows over a flat plate which is heated over the entire length. Which one of the following relationships between the hydrodynamic boundary layer thickness ( δ ) and the thermal boundary layer thickness ( δ t ) is true? (A) δ t > δ (B) δ t < δ (C) δ t δ (D) cannot be predicted ********** Published by: NODIA and COMPANY ISBN: 97889765
PAGE 66 FLUID MECHANICS CHAP 6 SOLUTION SOL 6. Option (A) is correct. From Darcy Weischback equation head loss h f D L V # #...() g Given that h 5 m, D. m, f. 5 Since volumetric flow rate νo Area # velocity of flow ( V) V νo. 6.7 m/ s Area π (.) 4 # (. ) Hence, h. 5 5 67 #. # # 9. 8 h 6. m - 6.8 m SOL 6. Option (C) is correct. Degree of reaction ( V V ) R ( V V ) + ( U U ) + ( W W ) where V and V are absolute velocities W and W are relative velocities U and U U for given figure Given W V, W V ( V V ) Hence R ( V V ) + ( U U ) + ( V V ) ( V V ) ( V V ) 5. SOL 6. Option (C) is correct. For flat plate with zero pressure gradient and Re (laminar flow). Boundary layer thickness & δ () x 49. x 49. x 49. x / Rex Vx V / υ υ δ \ x / For a same location ( x ) V δ \( V ) / Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 67 where V velocity of fluid δ δ V V b l / / / δ V V 4 V b l # δ b V l # V 4V (Given) / b 5. 4 l # SOL 6.4 Option (A) is correct. Takes point () at top and point () at bottom By Bernoulli equation between () and () V ( p+ p+ p) p+ ρgh+ ρgh+ ρgh+ g At Reference level () z and V at point () Therefore p V atm. + g & p+ ρgh+ ρgh+ ρgh p V atm. +...() g Since p atmospheric pressure (because tank is open) Hence p p atm. Therefore V g# [ ρgh+ ρgh+ ρgh] By Rearranging V ρgh ρgh g # ; + + h ρ g ρ g E ρh ρh ρh ρh g # ; + + h ρ ρ E gh # ; + + ρ h ρ h E SOL 6.5 Option (B) is correct. dy For Equipotential line, u Slope of equipotential line...(i) dx v For stream function, dy dx u v Slope of stream line...(ii) It is clear from equation (i) and (ii) that the product of slope of equipotential line and slope of the stream line at the point of intersection is equal to. u v # u v And, when mm, Then lines are perpendicular, therefore the stream line and an equipotential line in a flow field are perpendicular to each other. SOL 6.6 Option (C) is correct. Published by: NODIA and COMPANY ISBN: 97889765
PAGE 68 FLUID MECHANICS CHAP 6 Given : p a. kg/ m, ρ w kg/ m, x # m, g 9.8 m/ sec If the difference of pressure head h is measured by knowing the difference of the level of the manometer liquid say x. Then h x SG. w ρw : x SG. D : a ρ D a # :. D 8. m Where SG. SG. Weight density of liquid Weight density of water \ Density of Liquid Velocity of air V gh # 9. 8# 8..8 m/ sec SOL 6.7 Option (D) is correct. Given : p bar, p bar, ρ 99 kg/ m Isentropic work down by the pump is given by, W νdp m dp ρ W m dp ( ) ρ 99 # # 5 pascal 99. 9 Jkg /.9 kj/ kg ν m ρ SOL 6.8 Option (B) is correct. As shown in figure above. If point Bl is sufficiently far from B, these two forces (Gravity force and Buoyant force) create a restoring moment and return the body to the original position. A measure of stability for floating bodies is the metacentric height GM, which is the distance between the centre of gravity G and the metacenter M (the intersection point of the lines of action of the buoyant force through the body before and after rotation.) A floating body is stable if point M is above the point G, and thus GM is Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 69 positive, and unstable if point M is below point G, and thus GM is negative. Stable equilibrium occurs when M is above G. SOL 6.9 SOL 6. Option (C) is correct. In case of two parallel plates, when flow is fully developed, the ratio of V max and V avg is a constant. V max Vavg V max 6 m/sec V avg Vmax # 6 4 m/sec # Option (C) is correct. From Buckingham s π-theorem It states If there are n variable (Independent and dependent variables) in a physical phenomenon and if these variables contain m fundamental dimensions ( MLT,,, ) then variables are arranged into ( n m) dimensionless terms. Here n dimensional variables k Primary dimensions (M, L, T) So, non dimensional variables, & n k SOL 6. SOL 6. Option (B) is correct. Given : P kw, H 4 m, H 4 m If a turbine is working under different heads, the behavior of turbine can be easily known from the values of unit quantities i.e. from the unit power. So P u P / H P P / / H H / P H / P b H l # b 4 l # 5.6. 54 kw Option (D) is correct. Given : V xyi x zj P(,,) The vorticity vector is defined as, i j k Vorticity Vector x y z u v w Substitute, u xy, v x z, w i j k So, x y z xy x z Published by: NODIA and COMPANY ISBN: 97889765
PAGE 7 FLUID MECHANICS CHAP 6 i xz j ( xy) k ( xz) : ( xy) z ^ hd : + z D ; x y E x i + k[ xz x] Vorticity vector at P(,,), i+ k[ ] i 4k SOL 6. Option (C) is correct. Given : p 5 kpa, Z m, V m/sec, p kpa, Z m, ρ kg/ m, g 9.8 m/ sec Applying continuity equation at section S and S, AV AV V V D D so A A... (i) Applying Bernoulli s equation at section S and S with head loss h L, p V z ρ g + g + p V z hl ρg + g + + p z ρ g + p + z + h ρg L From equation (i) p p ^5 h# h L b + ( z z) ρg l + ( ) ( # 9. 8).58.6 m Head at section ( S ) is given by, p H + Z 5 # ρg + 5.9 m # 9. 8 Head at section S, p H + Z # ρg + 4.4 m # 9. 8 From H and H we get H> H. So, flow is from S to S SOL 6.4 Option (D) is correct. Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 7 Here type of flow is related to the dimensionless numbers (Non-dimensional numbers). So P. Compressible flow Y. Mach number Q. Free surface flow W. Weber number R. Boundary layer Z. Skin friction coefficient S. Pipe flow U. Reynolds number T. Heat convection V. Nusselt number So, correct pairs are P-Y, Q-W, R-Z, S-U, T-V SOL 6.5 Option (B) is correct. Given : p V 5 kpa, w 5 kn/ m ρg Consider steady, incompressible and irrotational flow and neglecting frictional effect. First of all applying continuity equation at section () and (). AV AV π ( d ) # V π ( d ) # V 4 4 Substitute the values of d and d, we get π ( ) V 4 # π ( ) V 4 # 4V V & V 4V...(i) Cavitation is the phenomenon of formation of vapor bubbles of a flowing liquid in a region where the pressure of liquid falls below the vapor pressure [ pl < pv] So, we can say that maximum pressure in downstream of reducer should be equal or greater than the vapor pressure. For maximum discharge p V p 5 kpa Applying Bernoulli s equation at point () and () p V z ρ g + g + p V z ρg + g + Published by: NODIA and COMPANY ISBN: 97889765
PAGE 7 FLUID MECHANICS CHAP 6 Here z z for horizontal pipe and w ρg 5 kn/ m 5 V 5 g + 5 5 5 5 5 ( 4V ) + From equation (i) V 4V 5 g 6V V g g 5 V g V. 4 # 9 8 5.4 m/sec 5 And V 4V 4 # 5.4.46 m/ sec Maximum discharge, Q max AV π ( d) V 4 π ( ). 46 4 # # π. 46 4 # #.6 m / sec SOL 6.6 Option (D) is correct. Given : P : u y, V x Q : u xy, V R : u x, V y For incompressible fluid, u + v + w x y z...(i) For irrotational flow ζ z, ζ z v u c x y m v u c x y m v u x y...(ii) From equation (i) and (ii), check P, Q and R For P : u y, u, u x y v x, v, v y x u + v x y & + (Flow is incompressible) Or, v u x y & 5! (Rotational flow) For Q : u xy u y u x x y Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 7 v v, v y x u + v x y & y Y (Compressible flow) Or, v u x y x & x Y (Rotational flow) For R : u x u, u x y v y v, v y x u + v x y Or, + & (Incompressible flow) v u x y & (Irrotational flow) So, we can easily see that R is incompressible and irrotational flow. SOL 6.7 Option (A) is correct. Given : L km m, D mm. m, Q.7 M / sec f., ρ kg/ m Head loss is given by, flv fl 4Q h f D# g D g # c πd m 6fLQ 8fLQ 5 5 π D # g π Dg Q πd 4 8. (. 7) # # # 5 (. 4) #(. ) #( 98. ). 784 6. m of water Pumping power required,. P ρgq # h f # 9. 8 #. 7 #. 6 75. 87.75 kw..8 kw # V SOL 6.8 Option (A) is correct. Published by: NODIA and COMPANY ISBN: 97889765
PAGE 74 FLUID MECHANICS CHAP 6 ur () R dp r 4μbdx lc R m Therefore, the velocity profile in fully developed laminar flow in a pipe is parabolic with a maximum at the center line and minimum at the pipe wall. The average velocity is determined from its definition, R V avg urrdr () R R dp r # # rdr R 4 dx μb lc R m dp r r dr R μbdx l # c R m dp r r 4 R dp R R μbdx l; 4R E 4 μbdx l; 4R E dp R R dp μbdx l # 4 8μbdx l Alternate Method : Now we consider a small element (ring) of pipe with thickness dr and radius r. We find the flow rate through this elementary ring. dq ( πr) # dr# u( r) Put the value of ur () dq ( r) dr R dp π r # # c 4μ mb dx lc R m Now for total discharge integrate both the rides within limit. Q & toq and R & tor So Q dq # R dp R π r r dr 4 μ bdx l c R m Q Q 4 R R dp r r 6 @ π 4μ bdx l; 4R E Now put the limits, we have Q R 4 dp π R R R dp R R 4 μ bdx l; 4R E π 4μ bdx l: 4 D 4 R dp π R R dp c 4 μ mbdx l: 4 D π 8μ bdx l Now Q Area # Average velocity A# V avg. 4 Q V R dp avg. π R dp A 8μ bdx l # πr 8μbdx l # SOL 6.9 Option (D) is correct. The continuity equation in three dimension is given by, ( ρu) + ( ρv) + ( ρw) x y z For incompressible flow ρ Constant Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 75 ρ u v w ; + + x y z E u + v + w x y z d : V So, the above equation represents the incompressible flow. SOL 6. None of these is correct. Given : ρ kg/ m, V m/sec, θ 8 6c, R.5 m Initial velocity in the direction of jet V Final velocity in the direction of the jet V cos θ. Force exerted on the bucket F x ρav6 V ( V cos θ) @ ρav6 + cos θ@ V Q( + cos θ) V Mass flow rate Q ρav Torque, T x Fx # R QV( + cos θ) R Torque per unit mass flow rate T x V ( + cos θ ) R ( + cos 6 c ). 5 Q # 7.5 N m/ kg/ sec And F y ρav( V sin θ) QV sin θ Torque in y-direction T y Fy # R R Total Torque will be T T + T 7.5 N m/ kg/ sec x y T x SOL 6. Option (A) is correct. Published by: NODIA and COMPANY ISBN: 97889765
PAGE 76 FLUID MECHANICS CHAP 6 Here Gap between moving and stationary plates are continuously reduced, so we can say that Volume of fluid moving out radially Volume of fluid displaced by moving plate within radius r Volume displaced by the moving plate Velocity of moving plate # Area V# πr...(i) Volume of fluid which flows out at radius r Vr # πr# h...(ii) Equating equation (i) and (ii), V# π r Vr # πrh Vr Vr Vh r & Vr h Alternate Method : Apply continuity equation at point (i) and (ii), AV AV V# π r Vr # πrh V r Vr h SOL 6. Option (B) is correct. From previous part of question, V r Vr h Acceleration at radius r is given by a r V dvr r # V d Vr r dr # dr : h D V V r #...(i) h At r R a r VR V V R h # h 4h SOL 6. Option (D) is correct. AV F D CD # ρ. ρav # C Re L Published by: NODIA and COMPANY ISBN: 97889765 D. Re L
CHAP 6 FLUID MECHANICS PAGE 77. blv VL ρvl # ρ # ReL ρ μ μ. # ρbv V ρ L...(i) μ So from equation (i) F D \ L...(ii) Drag force on front half of plate F L FD D/ From Equation (ii) Drag on rear half, F l D/ F D F D/ c FD m Now ratio of F D/ and F l D/ is FD FD/ F F > ld / c F D m SOL 6.4 Option (B) is correct. Given : v u L x b + l dx dt u L x b + u l ( L + x ) L dt u L # ( L x) dx + On integrating both the sides within limits t & tot and x & tol, we get t dt # u L L # ( L x) dx + t t L L 6@ ln( L+ x) u 6 @ t L ln 4L ln L u 6 @ L ln 4 u SOL 6.5 SOL 6.6 Option (A) is correct. Reynolds Number, Option (C) is correct. Re ρav μ V # A L # 5 IF.. VF.. Inertia force Viscous force ρvl μ Published by: NODIA and COMPANY ISBN: 97889765
PAGE 78 FLUID MECHANICS CHAP 6 Given figure shows the velocity triangle for the pelton wheel. Given : Flow velocity at Inlet V f flow velocity at outlet V f V f V u f (blade velocity) SOL 6.7 V V f u V w θ 9c From Inlet triangle, V ( Vf) + ( Vw) u a ( u ) u k + 5 4 Blade efficiency V V V 5 u u # 4 4 5 u 4 u 5 # 8% u 4 Option (C) is correct. u πdn gh 6 From this equation, H \ DN # DN H Constant So using this relation for the given model or prototype, c DN H m c DN H m p m Np Hp Dm N H #...(i) D m Published by: NODIA and COMPANY ISBN: 97889765 m p
CHAP 6 FLUID MECHANICS PAGE 79 Given : H m H 4 p, D m D p, Np N N N H D p p m # 4 H D # p p 4 So, N m N SOL 6.8 Option (B) is correct. For forced Vortex flow the relation is given by, V rω...(i) From equation (i) it is shown easily that velocity is directly proportional to the radius from the centre of the vortex (Radius of fluid particle from the axis of rotation) And also for forced vortex flow, ρω ( r r ) g( z z ) ρ ΔKE.. ΔPE.. & ΔKE. ΔPE.. Now total mechanical energy per unit mass is constant in the entire flow field. SOL 6.9 Option (A) is correct. List-I List-II P. Centrifugal compressor. Surging Q. Centrifugal pump. Priming R. Pelton wheel 4. Pure Impulse S. Kaplan Turbine. Axial Flow So, correct pairs are P-, Q-, R-4, S- SOL 6. Option (C) is correct. Let width of the channel b From mass conservation Flow rate at section A flow rate at B or Velocity A# Area of A Velocity at B# Area of B U #( H# b) Velocity for ( # y # δ ) # dy# b + velocity for ( δ # y # H δ) # dy# b + velocity for ( H δ # y # H) # dy# b δ y H δ H H y or U # H Vm# dy + V m dy + V m dy δ # # δ δ H δ Published by: NODIA and COMPANY ISBN: 97889765
PAGE 8 FLUID MECHANICS CHAP 6 or U # H V V ( H ) Vm δ m + m δ + δ U # H Vmδ+ Vm( H δ) Vm( δ+ H δ) or V m U H δ + H δ H H δ δ H SOL 6. SOL 6. Option (A) is correct. Applying Bernoulli s Equation at the section A and B. pa VA za ρ g + g + pb VB + + zb ρg g Here, z z So, A Substitute, B pa p ρg p p A B V V g B A pb VB VA V U ρ p A B ρu V m U ρu Option (C) is correct. p p A B U Vm ; U E m Vm Vm U b U l V B V and V U m A From previous part of question δ H 6 δ/ H@ From the Newton s law of Viscosity, the shear stress ( τ ) is directly proportional to the rate of shear strain ( du/ dy ). Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 8 So, τ \ du dy μ du dy Where μ Constant of proportionality and it is known as coefficient of Viscosity. SOL 6. SOL 6.4 Option (C) is correct. Convective Acceleration is defined as the rate of change of velocity due to the change of position of fluid particles in a fluid flow. In Cartesian coordinates, the components of the acceleration vector along the x -direction is given by. a x u + u u + v u + w u t x y z In above equation term u/ t is known as local acceleration and terms other then this, called convective acceleration. Hence for given flow. Convective acceleration along x -direction. a x u u + v u [ w ] x y Option (C) is correct. The velocity triangle for the pelton wheel is given below. Given : u u u m/ sec, V 5 m/ sec, Q. m / sec Jet deflection angle cc φ 8c c 6c ρqv [ w+ Vw ] u P # kw From velocity triangle, V w 5 m/ sec V...(i) V w Vr cos φ u V r Vr V u 5 cos 6c 5 5 m/ sec 5.5 m/ sec Published by: NODIA and COMPANY ISBN: 97889765
PAGE 8 FLUID MECHANICS CHAP 6 Now put there values in equation (i). [. ] P # 5 5 # kw.5 kw SOL 6.5 Option (D) is correct. Given : u x t, v xyt The velocity component in terms of stream function are ψ x v xyt...(i) ψ y u x t...(ii) Integrating equation (i), w.r.t x, we get # ψ ( xyt) dx xyt+ K...(iii) Where, K is a constant of integration which is independent of x but can be a function of y Differentiate equation (iii) w.r.t y, we get ψ xt+ K y y But from equation (ii), ψ xt y ψ Comparing the value of, we get y xt K + xt y K y K Constant( K ) From equation (iii) ψ xyt + K The line for which stream function ψ is zero called as stream line. So, xyt+ K K xyt If t is constant then equation of stream line is, xy K K t But in the question, there is no condition for t is constant. Hence, it is not possible to determine equation of stream line. Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 8 SOL 6.6 Option (D) is correct. Given : u u 4r u r oc o D m c R m Drop of pressure for a given length ( L) of a pipe is given by, μul r Δ p p p..(i) D (From the Hagen poiseuille formula) Where ur average velocity R And ur () R urrdr R # u r o rdr # R c R m R 4 R u o r r dr uo r r # R c R m R ; 4R E u 4 uo R R R ; 4R E u o R uo R : R 4 D Substitute the value of u in equation() μl So, Δ p uo 6μuL o # D D Note : The average velocity in fully developed laminar pipe flow is one-half of the maximum velocity. SOL 6.7 Option (C) is correct. In a steady and ideal flow of incompressible fluid, the total energy at any point of the fluid is constant. So applying the Bernoulli s Equation at section () and () p V Z ρ g + g + p V Z ρg + g + V Initial velocity at point () Z At the bottom surface Published by: NODIA and COMPANY ISBN: 97889765
PAGE 84 FLUID MECHANICS CHAP 6 p p p atm And z h h So, h h V V g gh ( h) V gh ( h) So, velocity of fluid is same inside the tube V p V g( h h ) SOL 6.8 SOL 6.9 Option (A) is correct. Given : P kw, N rpm, H 4 m d, H m d 4 Specific power for similar turbine is same. So from the relation, we have P / dh Constant For both the cases, P P / dh / dh / P d H / b P d l b H l # b 4 l b4 l # 4. Option (A) is correct. Net positive suction head, (NPSH) Pressure head + static head Pressure difference, Δ p ( 5) 5 kpa (Negative sign shows that the pressure acts on liquid in opposite direction) Δ p 5 # Pa.5 bar 5. #. m.95 m of water. Static head m (Given) Now, NPSH.95 +.95-4 m of water SOL 6.4 Option (B) is correct. Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 85 Given : U m/ sec, δ mm meter, ρ. kg/ m, B m and u Ua y δ k From the figure we easily find that mass entering from the side qp Mass leaving from the side qr + Mass Leaving from the side rs m pq ( mpq mrs) + mrs So, firstly Mass flow rate entering from the side pq is mo pq ρ # Volume ρ #( A# U) #( B# δ) # U Substitute the values, we get mo pq #( # )#. kg/ sec For mass flow through section r s, we have to take small element of dy thickness. Then Mass flow rate through this element, dmo ρ # Volume ρ #( A# u) ρ# u# B# ( dy) ρbua y dy δ k For total Mass leaving from rs, integrating both sides within the limits, dm & tom So, y & toδ m # dmo ρub # δ yb l dy 6 mo @ m mo mo rs δ ρub y δ ; E δ ρub δ δ # ρ UB δ # # # # 5#.5 kg/sec Mass leaving from qr o mo mo..5.5 kg/ sec m qr pq rs SOL 6.4 Option (D) is correct. Von Karman momentum Integral equation for boundary layer flows is, τ o ρ U θ x and θ momentum thickness δ # U u 9 U u Cdy So, τ o ρ U # δ x U u U u dy ; a k E U u y δ Published by: NODIA and COMPANY ISBN: 97889765
PAGE 86 FLUID MECHANICS CHAP 6 # δ y y dy x ; δa δk E Integrating this equation, we get y y x > c δ δ mh τ o And drag force on the plate of length L is, # L F D τo # b# dx δ # δ y y dy x c δ δ m G δ δ x c δ δ mg δ x : 6D SOL 6.4 SOL 6.4 Option (D) is correct. We know that potential flow (ideal flow) satisfy the continuity equation. The continuity equation for two dimensional flow for incompressible fluid is given by, u + v x y u v x y Option (D) is correct. Given : d mm. m, d 4 mm.4 m Δ p p p kpa Applying continuity equation at section () and (), AV AV π V A d c V 4 A m # V d 4 π d V V V # d b 4 l 4 V 4V..(i) Now applying Bernoulli s equation at section () and (), Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 87 p V z ρ g + g + p V z ρg + g + For horizontal pipe z z p p ρg V V g Δp V V ρ # ( 4V ) V 6V V 5V V # 4 & V m/sec 5 From equation (i) SOL 6.44 Option (A) is correct. It is a U -tube differential Manometer. In this manometer A and B at different level and the liquid contain in manometer has the same specific gravity (only mercury is fill in the manometer) Given : ρ mercury 6 kg/ m, g 9.8 m/ sec, Δ h 5 mm.5 meter Static pressure difference for U -tube differential manometer is given by, p p ρgh ( h) ρδ g h Hence p A A B A B 6 # 9. 8 #. 5. # Pa. kpa. kpa pb is positive and pa> pb, Flow from A to B. SOL 6.45 Option (B) is correct. Given : V 6 r b # m/sec π r l...(i) And V θ # m/sec π r...(ii) Dividing equation (i) by equation (ii), we get V r 6 # πr Vθ r # π # 5 V V r 5...(iii) In this equation (iii) V r Radial Velocity dr dt V θ Angular Velocity rω r dθ dt So, dr dt r dθ 5 dt Published by: NODIA and COMPANY ISBN: 97889765
PAGE 88 FLUID MECHANICS CHAP 6 dr r d θ 5 On integrating both the sides and put limits, between θ & toπ (for half revolution). r dr π # dθ r 5 # ln r r π 6 @ θ 56@ ln r ln [ π ] 5 ln r π 5 r π 5 e π/5. 5 r.5 # 64 meter r & to r and SOL 6.46 Option (B) is correct. Given : υ 7.4 # 7 m / sec, S.88, y.5 mm.5 # Density of liquid S # density of water. 88 # 88 kg/ m μ Dynamic viscosity Kinematic Viscosity υ ρ Density of liquid 7 μ υ# ρ 7. 4 # # 88 4 6.5 # Pa s From the Newton s law of viscosity, τ u 4 μ # 6. 5 5. y # # 5. #.65 Nm /.65 Pa meter SOL 6.47 Option (C) is correct. Given : V axi+ ayj...(i) The equation of stream line is, dx dy dz...(ii) ux uy uz Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 89 From equation (i), ux ax, uy ay and uz Substitute there values in equation (ii), we get dx dy ax ay dx x dy y Integrating both sides, we get dx dy # x # y log x log y+ log c log yc & x yc...(iii) At point (, ), c & c From equation (iii), x y & x y SOL 6.48 Option (C) is correct. In this question we have to make the table for calculate mean flow rate : Flow rate litres/ sec. Mean flow rate xi+ xf x b l Frequency f fx 7.5 to 7.7 7.6 7.6 7.7 to 7.9 7.8 5 9 7.9 to 8. 8. 5 8 8. to 8. 8. 7 9.4 8. to 8.5 8.4.8 8.5 to 8.7 8.6 86 Σ f 8 Σ fx 65.8 Mean flow rate, x Σfx Σf 65. 8 8.6 litres/ sec 8 SOL 6.49 Option (C) is correct. Published by: NODIA and COMPANY ISBN: 97889765
PAGE 9 FLUID MECHANICS CHAP 6 Flow rate, Q AV Q Q Q Inlet velocity, V A π ( R ) 4 A π d πr 4 Q Q Outlet Velocity, V A πr Therefore, resultant velocity will be, dv V V Q π ; R R E Acceleration at the exit section, a dv dt V dv dx In this case dv V V V V And dx L So, a Q Q Q # R R πr πl ; R R E π RL ; RR E Q ( R+ R)( R R) π RL RR G Considering limiting case R " R Then, a Q ( R R) R π RL RR G Q R R π RL 6 @ 5 Q ( R R) π RL 5 SOL 6.5 Option (D) is correct. Total thrust at the bottom of cylinder Weight of water in cylinder + Pressure force on the cylinder For rotating motion, p ρv ρr ω ρω r r r r p Pressure, V rω Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 9 And p ρω rdr Integrating both the sides within limits p between to p and r between to r, p # p # r ρω rdr 6@ p p r ρω r : D For calculating the total pressure on the cylinder, p r ρω r ρω # : D Dividing whole area of cylinder in the infinite small rings with thickness dr, Force on elementary ring ρω r Pressure intensity # Area of ring Total force, F # πrdr R ρω r R # rdr # π πρω # rdr 4 R r πρω R : 4 D πρω 4 Weight of water mg ρνg m ρν 4 ρπr Hg ρghπr A πr # 4 So, Net force ρghπr ρω π + R ρω R πr gh 4 ; +ρ 4 E SOL 6.5 Option (C) is correct. Given relation is, U U y y δ a δk and δ 464x....(i) Rex 5 U U m/sec, v.5 # m / s, ρ. kg/ m, L x Kinematic viscosity, μ υ ρ 5 μ υ# ρ 5. # #. 5.845 # kg/ m sec Reynolds Number is given as, ρux Re. x # # μ 5. # 5. 845 # δ 464. #.7 5. # And U U y y δ a δ k Published by: NODIA and COMPANY ISBN: 97889765
PAGE 9 FLUID MECHANICS CHAP 6 du dy U d y y dy y : δ aδkd U ; # δ δ E where U Free stream velocity U du c dy m U U : δd δ y We know that shear stress by the Newton s law of viscosity, τ du 5 μc dy m.845 U # # δ y Substitute the values of U and δ, we get 5. 845 # # # #. 7 45.8 # Nm / 5 4.6 # Nm / SOL 6.5 SOL 6.5 Option (B) is correct. Given : L 4 km 4 # 4 m, d. m f., V m/sec, H 5meter Head loss due to friction in the pipe, flv. 4 ( ) h f # # 4.77 m of water gd # 9. 8#. Now total pressure (absolute discharge pressure) to be supplied by the pump at exit Pressure loss by pipe + Head pressure of tank + Atmospheric pressure head Total pressure, p ρghf + ρgh + ρghatm p p ρgh [ f + H+ hatm] Pressure head, H & p Hρg ρg # 9. 8[ 4. 77 + 5 +. ] 5.5 # 5 Nm / 5.5 bar For water h atm. m Option (D) is correct. Given : p G 5. bar, p G. bar, p atm. bar Absolute pressure of G Atmospheric pressure + Gauge pressure. +.. bar Absolute pressure of G p G + p abs( G ) 5. +. 7. bar SOL 6.54 Option (A) is correct. Given : H 4.5 m, Q. m / sec, η 9%, N 4 rps 4 # 6 4 rpm η Shaft Power in kw Water Power in kw Published by: NODIA and COMPANY ISBN: 97889765 P ρ # g# Q# H b l
CHAP 6 FLUID MECHANICS PAGE 9 P η ρ g# Q# H # #. 9 # # 9. 8 #. # 4. 5 84.74 kw ρ water kg/ m For turbine Specific speed, N S N P 54 / 4 84. 74 54 / 5.8 rpm H ( 4. 5) Hence, 5 < N S < 55 for francis turbine. SOL 6.55 Option (B) is correct. List-I List-II P. Reciprocating pump. Positive Displacement Q. Axial flow pump 5. High Flow rate, low pressure ratio R. Microhydel plant. Plant with power output between kw to MW S. Backward curved vanes 6. Centrifugal pump impeller So, correct pairs are P-, Q-5, R-, S-6 SOL 6.56 Option (D) is correct. Given : Cross section area of body A Height of body H Density of body ρs Density of liquid ρ Tension in the string T We have to make the FBD of the block. B Buoyancy force From the principal of buoyancy, Downward force Buoyancy force m ρν T+ mg ρhag Published by: NODIA and COMPANY ISBN: 97889765
PAGE 94 FLUID MECHANICS CHAP 6 T+ ρν s g ρhag ν A# H T + ρ s AHg ρhag T ρhag ρ s AHg Ag( ρh ρ s H) SOL 6.57 Option (A) is correct. Given : Flow rate Q Velocity of water when it strikes the water surface U Total Mass (container + water) m Force on weighing balance due to water strike Change in momentum Δ P Initial Momentum Final momentum ρqu ρq() ρqu Final velocity is zero Weighing balance also experience the weight of the container and water. So, Weight of container and water mg Therefore, total force on weighing Balance ρqu + mg SOL 6.58 Option (D) is correct. First of all we have to take two section () and () Applying Bernoulli s equation at section () and (). p V z ρ g + g + p V z ρg + g + Published by: NODIA and COMPANY ISBN: 97889765
CHAP 6 FLUID MECHANICS PAGE 95 p V ρ + p V + z z ρ p ρ p ( V V )...(i) Apply continuity equation, we get AV π DV t 4 AV π DUV U. Let at point () velocity V 4 V D D b l # U...(ii) t Substitute the value of V from equation (ii) into the equation (i), ρ p p U D D 4 ρ U ; b l E U t D D 4 ; b le...(iii) t From the figure, we have Spring force Pressure force due to air kx As( p p) π D # ( p p ) 4 s D U 4 D D 4 π ρ s # ; b le From equation (iii) t 4 kx π D U D s ρ 8 ; b D l E x ρu k D D 4 πd 8 ; b l E t t s SOL 6.59 Option (B) is correct. Given : N 5 rpm, H meter, N rpm, Q 6 litres per minute From the general relation, U πdn gh 6 DN \ H & N \ D H Centrifugal pump is used for both the cases. So D N \ H H H N N D ( ) H N N # Η # m ( 5) The specific speed will be constant for centrifugal pump and relation is, N Q N s 4 / Constant H Published by: NODIA and COMPANY ISBN: 97889765
PAGE 96 FLUID MECHANICS CHAP 6 N Q N Q So, 4 / 4 / For both cases H H Q N N H / 4 4 / Q 5 # b H l # 6 # b l # / () 6 # # Squaring both sides Q 8 6 litre/ min 4 # # Alternate : From unit quantities unit speed N N u H H N H N N H N H N H or H N H ( ) N # # m ( 5) Q Q Unit discharge Q u H H Q Q H H Q H or Q 6 # litre/ min H SOL 6.6 None of these is correct. List-I List-II P. Curtis. Velocity compounding Q. Rateau 4. Pressure compounding R. Kaplan 6. Axial flow turbine S. Francis 7. Mixed flow turbine So, correct pairs are P-, Q-4, R-6, S-7. SOL 6.6 Option (B) is correct. Given : L mm, d mm, D mm, V mm/ sec We have to take the two sections of the system () and (). Published by: NODIA and COMPANY ISBN: 97889765