# The online of midterm-tests of Fluid Mechanics 1

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1 The online of midterm-tests of Fluid Mechanics 1 1) The information on a can of pop indicates that the can contains 460 ml. The mass of a full can of pop is 3.75 lbm while an empty can weights 80.5 lbf. Determine the specific weight, density and specific gravity of pop. Express your results in BG unit. Answer: γ = lb/ft 3, ρ = slug/ft 3 and SG = ) A tank of oil has a mass of 30 slugs. (a) Determine its weight in pounds and in newtons at the earth s surface. (b) What would be its mass (in slug) and its weight (in pound) if located on the moon s surface where the gravitational attraction is approximately one-sixth that at the earth s surface? Answer: (a) 966 lb and 4290 N, (b) 161 lb. 3) A liquid when poured into a graduated cylinder is found to weight 8 N when occupying a volume of 500 ml (milliliters). Determine its specific weight, density, and specific gravity. Answer: γ = 16 kn/m 3, ρ = kg/m 3 and SG = ) Initially when 1000 ml of water at 10 o C are poured into a glass cylinder the height of the water column is 1000 mm. The water and its container are heated to 70 o C. Assuming no evaporation, what then will be the depth of the water column (h) if the coefficient of thermal expansion for the glass is mm/mm per o C? Let: ρ = kg/m 3 for 10 o C and ρ = kg/m 3 for 70 o C. Answer: h 70 C = mm. 5) A space 16 mm wide between two large plane surface is filled with SAE 30 Western lubricating oil at 35 o C. What force F is required to drag a very thin plate of 0.4 m 2 area between the surface at a speed v = 0.25 m/s (a) if this plate is equally spaced between the two surface? (b) If t = 5 mm? Let: μ at 35 C = 0.81 N s/m 2 Answer: (a) 4.5 N (b) 5.24 N. Fig. 5

2 6) A piston of weight 21 lb slides in a lubricated pipe, as shown in Fig 6. The clearance between piston and pipe is in. If the decelerates at 2.1 ft/s 2 when the speed is 21 ft/s, what is the viscosity of the oil? Answer: μ = lb s/ft 2. 7) A piston having a diameter of 5.48 in and a length of 9.5 in slides downward with a velocity v through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is in and the cylinder weights 0.5 lb. Estimate v if the oil viscosity is lb s/ft 2. Assume the velocity distribution in the gap is linear. Answer: v = ft/s. 8) A 40 lb, 0.8 ft diameter, 1 ft tall cylinder tank slides slowly down a ramp with a constant speed of 0.1 ft/s asshowninfig shown Fig. 8. The uniform thickness oil layer on the ramp has a viscosity of 0.2 lb s/ft 2. Determine the angle θ of the ramp. Answer: θ = 7.22 o. Fig. 8 9) Assume that the surface tension force act at an angle θ relative to the water surface as shown in Fig. 9. (a) The mass of the double-edge blade is kg, and the total length of its sides is 206 mm. Determine the value of θ required to maintain equilibrium between the blade weight and the resultant surface tension force. (b) The mass of the single-edge blade is kg, and the total length of its sides is 154 mm. Answer: (a) θ = 24.5 o, (b) T sinθ = sinθ. Fig. 9(a) Fig. 9(b)

3 10) Find the pressure at A, B, C and D in Fig. 9. Answer: P A = 374 lb/ft 2, P B = 125 lb/ft 2, P C = P B and P D = 624 lb/ft 2. 11) In Fig. 11 assume the following: atmospheric pressure = 930 mbar (abs); vapor pressure of the alcohol = 110 mbar (abs) x =3.3 m and y = 1.6 m. Compute the reading (a) on the pressure gage and (b) on the manometer. Fig. 10 Fig. 11 Answer: (a) P A, gage = 397 mmhg (vacuum), (b) P manometer = 437 mm. 12) The cylindrical tank with hemispherical ends shown in Fig. 12 contains a volatile liquid and its vapor. The liquid density is 800 kg/m 3, and its vapor density is negligible. The pressure in the vapor is 120 kpa (abs), and the atmospheric pressure is 101 kpa (abs). Determine (a) the gage pressure reading on the pressure gage and (b) the height h of the mercury manometer. Answer: (a) P gage = 26.9 kpa, (b) h = m. Fig ) A closed cylindrical tank filled with water has a hemispherical dome and is connected to an inverted piping system as shown in Fig. 13. The liquid in the top part of the piping system has a specific gravity of 0.8, and the remaining parts of the system are filled with water. If the pressure gage reading at A is 60 kpa, determine: (a) the pressure in pipe B, (b) the pressure head (in mmhg) at the top of the dome (C). Fig. 13 Answer: (a) P B = 103 kpa, (b) h C = 230 mmhg.

4 14) The inclined differential manometer of Fig. 14 contains carbon tetrachoride. Initially the pressure differential between pipes A and B, which contain a brine (SG = 1.1), is zero as illustrated in the figure. It is desired that the manometer give a differential reading of 12 in (measured along the inclined tube) for a pressure differential of 0.1 psi. Determine the required angle of inclination θ. Fig. 14 Answer: θ = 27.8 o. 15) Gate AB in Fig. 15(a) is 16 ft long and 8 ft wide. Neglecting the weight of the gate, (a) compute the water level h for which the gate will start to fall, (b) recomputed the level h by including the weight of the 2 in thick steel which SG steel = Answer: (a) h = 11.7 ft, (b) h = 10.7 ft. Fig. 15(a) Fig. 15(b) 16) The common type of irrigation head gate shown in Fig. 16 is a plate that slides over the opening to a culvert. The coefficient c e of friction between the gate and its sliding ways is 0.6. Find the force required to slid open this 600 lb gate if it is set (a) vertically, (b) on a 2:1 slop (n=2), as is common. Answer: (a) T = 8990 lb, (b) T = 8310 lb. Fig. 16(a) Fig. 16(b)

5 17) A tank with vertical ends contains water and is 6 m long normal to the plane of Fig. 17. The sketch shows a portion of its cross-section where MN is one-quarter of an ellipse with smilaxes b and d. If a = 1.0 m, b = 2.5 m and d = 4 m, find, for the surface represented by MN, the magnitude and position of the line of action of (a) the horizontal component of force, (b) the vertical component of the force, (c) the resultant force and its direction relative to the horizontal. Fig. 17 Answer: (a) h cp = 3.44 m below surface, (b) x cg = m, (c) F R = 933 N and θ = 40.8 o. 18) The rigid gate, OAB, of Fig. 18 is hinged at O and rests against a rigid support at B. What minimum horizontal force, P, is required to hold the gate closed if its width is 3 m? Neglect the weight of the gate and friction in the hinge. The back of the gate is exposed to the atmosphere. Fig. 18 Answer: P = 436 kn. 19) Three gates of negligible weight are used to hold back water in a channel of width b as shown in Fig. 19. The force of the gate against the block for gate (b) is R. Determine (in term of R) the force against the blocks for the other two gates. Answer: F B (a) = 1.17R, F B, (c) = 0.875R. Fig. 19

6 20) The hydrometer shown in Fig. 20 has a mass of kg and the cross-section area of its stem is 290 mm 2. Determine the distance between graduations (on stem) for specific gravities of 1.0 and 0.9. Answer: Δh = 17.2 mm. Fig ) A velocity field is given by V = Axi Ayj, the units of velocity are m/s; x and y are given in meters; A = 0.3 s. (a) Obtain an equation for the streamlines in the xy plane, (b) Plot the streamline passing through hthe point t( (x 0, y 0 ) = (2, 8), (c) Determine the velocity of a particle at the point (2,8), (d) If the particle passing trough the point (x 0, y 0 ) is marked at time t = 0, determine the location of the particle at time t = 6 s, (e) What is the velocity of this particle at time t = 6 s, (f) Show that the equation of the particle path (the pathline) is the same as the equation of the streamline. Answer: (a)lny= -ln x C, (b) xy = x 0 y 0 = 16 m 2, (c) V = 0.6i 2.4j m/s, (d) x = 12.1 m and y = 1.32 m, (e) V = 3.63i j m/s, (f) e At = y 0 /y = x/x 0. 22) The velocity in a certain two-dimensional flow field is given by the equation V = 2xt i + 2yt j, where the velocity is in ft/s when x, y and t are feet and seconds, respectively. Determine expressions for the local and convective components of acceleration in the x and y directions. What is the acceleration at the point x = y = 2 ft at the t = 0 s? Answer: a x, local = 2x, a x, convect = 4xt 2, a = 5.66 ft/s 2. 23) For the solid-propellant rocket in Fig. 23, compute the rate of mass loss of the propellant, assuming the exit gas has a molecular weight of 30. Answer: dm/dt = kg/s. Fig. 23

7 24) The open tank in the Fig. 24 contains water at 20 C. For incompressible flow, (a) derive an analytic expression for dh/dt in terms of (Q 1, Q 2, Q 3 ), (b) If h is constant, determine V 2 for the given data if V 1 = 3 m/s and Q3 = 0.01 m 3 /s. Answer: (a) dh/dt = [Q 1 + Q 2 + Q 3 ] / [πd 2 /4], (b) V 2 = 4.13 m/s. Fig ) Consider the steady flow in a water pipe joint shown in the diagram. The areas are: A 1 = A 2 = 0.2 m 2 and A 3 = 0.15 m 2. In addition, fluid is lost out of a hole at point 4, estimated at a rate of 0.1 m 3 /s. The average speeds at sections point 1 and 3 are V 1 = 5 m/s, V 3 = 12 m/s, respectively. Find the velocity at section point 2. Fig. 25 Answer: V2 = 4.5 m/s. 26) Water at 20 C flowa through a 5 cm diameter pipe which has a 180 o vertical bend, as in Fig. 26. The total length of pipe between flanges 1 and 2 is 75 cm. When the weight flow rate is 230 N/s, P1 = 165 kpa an p2 = 134 kpa. Neglecting g pipe p weight, determine the total force which the flanges must withstand for this flow. Fig. 26 Answer: F x, flange = 750 N and F y, flange = 14 N. 27) Determine the magnitude and direction of the x and y components of the anchoring force required to hold in place the horizontal 180 o elbow and nozzle combination shown in Fig. 27. Also determine the magnitude and direction of the x and y components of the reaction force exerted by 180 o elbow and nozzle on the flowing water. Answer: F Ax = 1890 lb, F Ay = 0, F x = 1890 lb, F y = 0. Fig. 27

8 28) A 20 o C water jet strikes a vane on a tank with frictionless wheels, as shown. The jet turns and falls into the tank without spilling. If θ = 30 o, estimate the horizontal force F needed to hold the tank stationary. Answer: F = 106 lb. Fig ) Water at 20 o C exits to the standard sea-level atmosphere through the spit nozzle in Fig. 29. Duct areas are A 1 = 0.02 m 2 and A 2 = A 3 = m 2. If P1 = 135 kpa (abs) and the flow rate is Q 1 = Q 3 = 275 m 3 /h, compute the force on the flange bolts at section 1 Fig. 29 Answer: F bolt = 3100 N. 30) A metal container 2 ft high, with an inside cross-sectional area of 1 ft 2, weight 5 lb when empty. The container is placed on a scale and water flows in through an opening in the top and out through the two equal-area openings in the sides as shown in the diagram. Under steady flow conditions, the height of the water in the tank is h = 1.9 ft. What does the scale indicate? Fig. 30 Answer: F y = 143 lb. 31) A small lawn sprinkler is shown in the sketch below. At an inlet gage pressure of 20 kpa, the total volume flow rate of water through the sprinkler is 7.5 lpm and it rotates at 30 rpm. The diameter of each jet is 4 mm. Calculate the jet speed relative to each sprinkler nozzle. Evaluate the friction torque at the sprinkler pivot. Answer: T f = N m. Fig. 31 Good Luck: By Dr. Bundit Krittacom

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