FLUID MECHANICES LAB:I


 Roxanne Phyllis Porter
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1 Force Area Length FLUID MECHANICES LAB:I Experiment:0 Measurement of viscosity by Redwood viscometer. Aim:  To determine the kinematic viscosity of a liquid and its variation with temperature. Apparatus: Redwood viscometer with its accessories such as a flask, ball valve, etc. Heating arrangement, Thermometer, Stopwatch, Oil etc. Theory: It is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of fluid. When two layers of fluid, a distance dy apart, move one over the other at different velocities, say u and u+ du as shown in figure, the viscosity together with relative velocity causes a shear acting between the fluid layers. The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to y. It is denoted by (Tau) Mathematically, du τ dy Figure:Velocity Variation near a Solid Boundary. Where is the constant of proportionality and is known as the coefficent of dynamic viscosity or only viscosity, represents the rate of shear strain or rate of shear deformation or velocity gradient.. Thus viscosity is also defined as the shear stress required to produce unit rate of shear strain. Units of Viscosity: Shear stress μ Change of velocity Change of distance In MKS units, In CGS units, In SI units, Pascal N/, Conversion: kgf 9.8 N Time Lengt h Kgfsec / [Unit Force Time Length of force kilogramforce (kgf)] dynesec / [Unit of force dyne] Nsec / [Unit of force Newton] Nsec / Pas Kgfsec / 9.8 Nsec/ Force mass x acceleration, N kg x m/ SRCOE, Lonikand. Civil Engineering Department Page
2 FLUID MECHANICES LAB:I N 000 gm x 00 cm / N 000 X 00 X gmcm/ N 000 X 000 X dyne, N sec/ 000 x 00 x dynesec/ kgfsec/ 9.8 x 000 x 00 x dynesec/ dynesec/ dynesec/ poise kgfsec/ 98. poise N sec/ 9. 8 x kgfsec/ 9. 8 x 98. poise 0 poise. Kinematic viscosity (v): It is defined as the ratio of dynamic viscosity to the density of the fluid. Mathematically, In MKS and SI units, In CGS units,, Stroke. Effect of Temperature on Viscosity: ) The viscosity of both liquids and gases will vary with temperature but in different manner. ) In case of liquids, the viscosity is due to cohesion. When the temperature of liquid increases, the volume of fluid increases and hence the distance between molecules increases with decreases the cohesion. Therefore, the viscosity of liquid decreases with increases in temperature. 3) In case of gases, viscosity is due to molecular momentum exchange. When the temperature of gas increases, kinetic energy of molecules increases and hence molecular momentum exchanges increases. Therefore, the viscosity of gases increases with increases in temperature. Experimental SetUp: The redwood viscometer consists of vertical cylindrical oil cup with an orifice in the centre of its base. The orifice can be closed by a ball. A hook pointing upward serves as a guide mark for filling the oil. The cylindrical cup is surrounded by the water bath. The water bath maintains the temperature of the oil to be tested at constant temperature. The oil is heated by Figure: Redwood Viscometer. heating the water bath by means of an immersed electric heater in the water bath; the provision is made for stirring the water, to maintain the uniform temperature in the water bath and to place the thermometer to record the temperature of oil and water bath. The cylinder is 47.65mm in diameter and 88.90mm deep. The orifice is.70mm in diameter and mm in length, this viscometer is used to determine the kinematic viscosity of the oil. From the kinematic viscosity the dynamic viscosity is determined.
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4 FLUID MECHANICES LAB:I Procedure:. Level the Viscometer with help of levelling screws.. Fill the water jacket with water and heat it to the desired temperature by using electric heater provided around the water jacket. 3. Close the orifice by means of a ball valve and pour the oil whose viscosity is to be determined into the cylinder up to the index mark. 4. Record the temperature of oil and keep the measuring flask below the orifice. 5. Lift the valve and start the stop watch simultaneously. 6. Measure the time in seconds required to collect 50 cc of oil to various temperatures. Observation: Table:0 Sr.no Temperature Time Kinematic viscosity (t) (T) ( ) Sec cm /sec Specifications: AConstant0.00 B Constant 0.8 T Time taken in seconds to collect 50cc of liquid. Calculation: Sample Calculation for First Reading: Kinematic viscosity of liquid, γ (A x T) (B / T) Significance: Viscosity affects heat generation in bearings, cylinders and gear sets related to oil s internal friction. It governs the sealing effect of oils and the rate of oil consumption, as well as determines the ease with which machines may be started or operated under varying temperature conditions, particularly in cold climates. Not all oils respond in the same way to a given change in temperature. Many oils contain an ability to resist changes in viscosity due to a change in temperature. This property is referred to as the oil's viscosity index or VI. The higher the VI of oil, the less its viscosity is altered by temperature changes. Another factor in the measurement of viscosity is the ability of oil to resist shearing or the "tearing away of one plane of lubricant from another" during the hydrodynamic lubrication function. The benefits of oils with a higher VI are:
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6 FLUID MECHANICES LAB:I. A general increase in viscosity at higher temperatures, which results in lower oil consumption and less wear.. A reduced viscosity at lower temperatures, which will improve starting and lower fuel consumption. Graph: Draw a graph Temperature Vs Kinematic viscosity. Result:. Viscosity is at the temperature. Viscosity is at the temperature 3. Viscosity is at the temperature 4. Viscosity is at the temperature Conclusion: By observing the readings/ Graph, it is come to know that the viscosity goes on decreases with the increase in temperature.
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8 FLUID MECHANICES LAB:I Experiment:0 Measurement of Pressures Using Different Pressure Measuring Devices. Aim: To measure pressure of a flowing fluid by different pressure measuring devices. Apparatus. Manometer, Pressure gauge etc., Theory: Pressure at a point is defined as the total force exerted on a plane perpendicular to it. Mathematically, P where F Total force, A Total area The units of pressure in: MKS units kgf/ and kgf/cm SI units N/m and Pascal and represented by Pa. Other commonly used units of pressure is bar N/m The pressure is measured in two different systems. In one system, it is measured above the absolute zero or complete vacuum and it is called the absolute pressure and in other system pressure above the atmospheric pressure and it is called gauge pressure. Thus: Absolute Pressure: It is defined as the pressure which is measured with reference to absolute vacuum pressure. ) Gauge Pressure: It is defined as the pressure which is measured with the help of a pressure measuring instrument, in which the atmospheric pressure is taken as datum. The atmospheric pressure on the scale is marked as zero. ) Vacuum Pressure: It is defined as the pressure below the atmospheric pressure. The relation between the absolute pressure, gauge pressure and vacuum pressure are, Mathematically:. Absolute Pressure Atmospheric Pressure + Gauge Pressure.. Vacuum PressureAtmospheric Pressure Absolute Pressure Note: The Atmospheric pressure at sea level at 5 0 C IS 0.3 or 0.3 in SI units. Measurement of Pressure: The pressure of fluid can be measured by the following devices.. Manometers and. Mechanical Gauges. Manometers. These are defined as the devices used for measuring the pressure at a point in a fluid by balancing the column of fluid by the same or another column of the fluid. T hey are classified as: SRCOE, Lonikand. Civil Engineering Department Page 5
9 FLUID MECHANICES LAB:I Simple Manometers and Differential Manometers. Simple Manometers: A simple manometer consists of a glass tube having one of its ends connected to a point where pressure is to be measured and other end remains open to atmosphere. Common types of simple manometers are: ) Piezometer, ) Utube Manometer and 3) Single Column Manometer. Piezometer: It is the simple type of manometer used for measuring gauge pressure. One end of the manometer is connected to the point where pressure is to be measured and other end is open to the atmosphere as shown in figure. The rise of liquid is say h in piezometer tube, and then pressure at A is given by, Figure:Piezometer. Utube Manometer: Pressure at A It consists of glass tube bent in Ushape, one end of which is connected to a point at which pressure is to be measured and other end remains open to the atmosphere as shown in figure. The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of liquid whose pressure is to be measured. For gauge pressure: Let B is the point at which pressure is to be measured, whose value is P. The datum line is AA Let Height of liquid above the datum line, h Height of heavy liquid above the datum line, S Specific gravity of light liquid, ρ Density of light liquid 000 Figure: Utube manometer. S Specific gravity of heavy liquid, ρ Density of heavy liquid 000 Pressure in left column Pressure in right column above datum line above A A above datum line A A + P For Vacuum Pressure: For measuring vacuum pressure, the level of the heavy liquid in the manometer will be as shown in figure (b). Then ++ 0 P +
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11 + FLUID MECHANICES LAB:I Single Column Manometer: Single column manometer is a modified form of a Utube manometer in which a reservoir, having a large crosssection area about 00 times as compared to the area of the tube is connected to one of the limbs (say left limb) of the manometer as shown in figure. Due to large cross section area of the reservoir, for any variation in pressure, the change in the liquid level in the reservoir will be very small which may be neglected and hence the pressure is given by the height of liquid to the other limb. The other limb may be vertical or inclined. ) Vertical Single Column Manometer. ) Inclined Single Column Manometer. Figure: Single Column Manometer. Vertical Single Column Manometer. Figure (a) shows the vertical column manometer. Let XX is the datum line in the reservoir and in the right limb of the manometer, when it is not connected to the pipe. When the manometer is connected to the pipe, due to high pressure at A', the heavy liquid in the reservoir will be pushed downward and will rise in the right limb. Let Fall of heavy liquid in reservoir, Rise of heavy liquid in the right limb, Height of centre of pipe above XX PA Pressure at A which is to be measured, A Cross section area of the reservoir, a Crosssection area of the right limb, S Specific gravity of liquid in pipe, S Specific gravity of heavy liquid in reservoir and right limb, ρ Density of liquid in pipe, ρ Density of liquid in reservoir. Fall of heavy liquid in reservoir Rise of heavy liquid in right limb Now consider the datum line YY as shown in figure (a). Then pressure in the right limb above YY ( + ) Pressure in the left limb above YY + + Equating these pressures, we have ( + ) + + ( ) + Now substuting, in the above equation, we get As the area A is very large as compared to a, hence ratio neglected. becomes very small and can be SRCOE, Lonikand. Civil Engineering Department Page 7
12 FLUID MECHANICES LAB:I g () From above equation (), it is clear that as h js known and hence by knowing h or rise of heavy liquid in he right limb, the pressure at A can be calculated. Inclined Single Column Manometer. Figure: (b) shows the inclined single column manometer. This msnometer is more sensitive. Due to inclination the distance moved by the heavy liquid in the right limb will be more. Let L Length of heavy liquid moved in right limb from XX inclination of right limb with horizontal, h Vertical rise of heavy liquid in right limb from XX L sin From equation () g PA sin X Differential Manometers: Differential manometers are the devices used for measuring the difference of pressures between two points in a pipe or in two different pipes. A differential manometer consists of a Utube, constaining a heavy liquid, whose two ends are connected to the points, whose difference ofpressure is to be measured. Most commenly types of differential manometers are: ) Utube differential manometers and ) Inverted Utube differential manometers. Utube Differential Manometer: Figure: (a) showes the differential manometer of Utube type. In figure (a), the two points A and B are at different level and also contains liquid of different specific gravity. These points are connected to the tube differential Figure: manometer. Let the pressure at A abd B are Figure:Utube differential manometers PA and PB, Let h Difference of mercury level in the Utube, Y Distance of the centre of B, from the mercury level in the right limb, X Distance of the centre of A from the mercury level in the right limb, ρ Density of liquid at A, ρdensity of liquid at B. ρg Densty of heavy liquid or mercury. Taking datum line as XX, PA PB ρg g h ρgy ρg h + x P P h g (ρ g A B ρ ) + Difference of pressure at A and B h g (ρ ρ ) + g SRCOE, Lonikand. Civil Engineering Department Page 8
13 FLUID MECHANICES LAB:I In figure (b): In figure (b), the two points A and B are at the same level and contains the same liquid of density. Then Pressure above datum line X X in the left limb Pressure above datum line X X in the left limb + + PA PB g h ρg ρ Inverted Utube Differential Manometer: + It consists of an inereted Utube, containg a light liquid. The two ends of the tube are connected to the points whose difference of pressure is to be measured. It is used for measuring difference of low pressures as shows the above jnverted U tube differential manometer connected to the two points A and B. Let the pressure at A is more than the pressure at B. Figure:Inverted UTube Differential Manometer. h Difference of light liquid, ρ Density of liquid at A, ρ Density of liquid at B, ρs Density of light liquid, PA Pressure at A, Let Height of liquid in left limb below the datum line XX h Hight of liquid in the right limb, PB Presure at B. Taking XX as datum line. Then pressure in the left limb below XX PA Pressure in the right limb below XX Equating the above two pressure, we get Mechanical Gauges: These are defined as the devices used for measuring the pressure by balancing the fluid column by the spring or dead weight. The commonly used mechanical pressures are: ) Diaphragm pressure gauge, ) Bourdon tube pressure gauge, 3) Dead weight pressure gauge and 4) Bellow pressure gauge. Experimental SetUp: Different types of pressure measuring instruments are arranged and connected to the pipe where pressure is to be measured. Procedure: ) Connect the instrument to the pipe through which water is flowing. SRCOE, Lonikand. Civil Engineering Department Page 9
14 FLUID MECHANICES LAB:I ) Record the reading in the manometer and pressure gauge. 3) By changing the discharge in the pipe, again note down the readings of manometer and pressure measuring gauges. Observation Table:0 Sr.no Manometric Reading Calculated pressure Pressure in gauge in Difference. In cm of Hg P P ( ) P P Cm Cm Cm in Calculation: Sample Calculation for First Reading: 760 mm of Hg Bar. For 4 mm of Hg, 760 Significance: () For measurement of pressure at ground seepage. () For measuring pressure in chemical plants and water treatment plants. Graph: Draw a graph Vs Pressure gauge reading Result. Conclusion: By measuring any pressure measuring instrument, the pressure comes to be same.
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16 FLUID MECHANICES LAB:I Experiment:03 Determination of stability of floating bodies using ship models. Meta centre height of ship model. Aim: To determine the stability of floating bodies using ship models. Apparatus: Model of ship, Tank with water, Weight, etc., Theory: Principle of floatation Consider a body is floating in water when the weight of the body is more than the up thrust then the body will sink down in water. But if the weight is equal to the up thrust of the liquid the body will float in the water. The weight of the body is equal to the upward thrust of the liquid on the body. This concept is called as Principle of floating. Figure:Floating Body. Buoyancy: When a body is immersed in a fluid an upward force is exerted by the fluid on the body. This upward force is equal to the weight of the fluid displaced by the body and is called the force of buoyancy or buoyancy. Arenumedes Principle: It states that whenever a body is immersed wholly or partly in fluid, the resultant force acting on it, is equally to the difference between the upward pressure of the fluid on its bottom and the downward force due to gravity. MetaCentre: It is defined as the point about which a body starts oscillating when the body is tilted by a small angle. The metacentre may also be defined as the point at which the line of action of the force of buoyancy will meet the normal axis of the body when the body is given a small angular displacement. Consider a body floating in a liquid as shown in figure. Let the body is in equilibrium and G is the centre of gravity and B the centre of buoyancy. For equilibrium, both the points lie on the normal axis, which is vertical. Let the body is given a small angular displacement in the clockwise direction as shown in figure. The Figure:  MetaCentric Height. centre of buoyancy, which is the centre of gravity of the displaced liquid or centre of gravity of the portion of the body submerged in liquid, will now be shifted towards right from the normal axis. Let it is at B as shown in figure. The line of action of the force of buoyancy in this new position will intersect the normal axis of the body at some point say M. This point M is called Metacentre. MetaCentric Height: The distance between the metacentre of a floating body and the centre of grvity of the body is called metacentric height. i.e. MG. Experimental setup: SRCOE, Lonikand. Civil Engineering Department Page
17 FLUID MECHANICES LAB:I A vessel is attached with a protector and a plumb, a horizontal scale on the vessel, a container filled water, and weights. Procedure: ) Fill the tank with water. ) Keeps the ship floating over the water. 3) See that plumb indicates zero reading. 4) Place the weight on the deck. 5) Measure the displacement of weight and angle indicated by plumb bob. 6) Repeat the procedure for different displacement of weight. Observation: Table:03 Sr. no. Displacement of applied Tilt angle θ Applied weight Metacentric weight X w height MH M Calculation: Sample Calculation for First Reading: Metacentre Height: MH Where kg M W Weight of vessel including weight applied w 3.0 kg N S Distance from its centre of gravity. w Weight applied on one side of ship, Angle of tilt of ship. Significance: Why to find Metacentre height? It is necessary for the stability of a floating body, if metacentre is above centre of gravity, body will be stable because the restoring couple produced will shift the body to its original position. It is a function of the configuration of a ship and the distribution of its weight. Because it can be determined relatively easily and quickly, either by empirical relations or by direct calculation, it is often relied upon as a principal indication of the stability of the ship and its ability to survive extensive flooding due to underwater damage. Result: Conclusion: SRCOE, Lonikand. Civil Engineering Department Page
18 + + FLUID MECHANICES LAB:I Experiment:04 Experimental verification of Bernoulli s theorem with reference to loss of energy. Aim: To verify Bernoulli s theorem with reference to loss of energy. Apparatus: A taper (ConvergingDiverging) rectangular pipe fitted with piezometer tubes fitted at different section), Water supply tank, Measuring tank, Stop watch, Scale, etc., Theory: Statement: It states that in a steady, ideal flow of an incompressible fluid, the total Energy at any point of the fluid is constant. The total energy consists of pressure energy, Kinetic energy and potential energy or datum energy. These energies per unit weight of the fluid are, Pressure energy Kinetic Energy Datum Energy Z Mathematically, Bernoulli s theorem is written as, + + Z Constant. Assumptions: The following assumptions are made in the derivation of Bernoulli s equation. The fluid is ideal. I.e. Viscosity is zero. The flow is steady. The flow is incompressible. The flow is irrotational. Bernoulli s Equation for Real Fluids: The Bernoulli s equation is derived on the assumption that fluid is nonviscous and therefore frictionless. But all the real fluids are viscous and hence offer resistance to flow. The Bernoulli s equation for real fluids between points () And () is given as + + Where Loss of Energy between points () and (). Experimental Set Up: ) The apparatus consist of convergingdiverging dust of 750 mm length through which water is discharging to delivery tank. ) Parallel piezometric tubes are fitted at small interval to show the pressure head at different sections. 3) The board on which the piezometric tube is fixed is graduated, so as to ease the procedure of taking piezometric reading. 4) The discharge is measured by collecting water in the measuring tank. 5) Water is supplied to the supply tank by pump which can be regulated by inlet valve.
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20 FLUID MECHANICES LAB:I Procedure: ) Connect the water pipe to the valve. ) Adjust the flow with the help of a gate valve. 3) Now allow the levels in the piezometer to stable and note down the heads 4) Close outlet valve of measuring tank and measure the time to rise water level by 0 cm (Discharge of flow). 5) Now repeat the procedure by changing the discharge. Observation: Table:04 Taperi Cross sectional ( ) in Rise of Pressure Sectional Velocity Total head ng area of meters water in head Velocity head (P/ρ g) + Sr. Piezometer Piezomet g ( /g) No. er In metre In metre. ( + ) () In metre In meters x x x x x x x x x x x x x x Specifications: Area of tank 0.3m x 0.3m Rise of water in tank 0cm 0.meter Volume of water collected in tank 0.3m x0.3m x 0.m Time required in collecting 0 cm rise of water in the tank. Sample Calculation for First Reading: Discharge: (Volume of water)/ (Time required to collect water in water tank for 0 cm rise) (Area of tank x Rise of water level)/t (0.3M X 0.3M X 0.M) / T Area of tube x velocity Section Velocity V / (Area of tube) Velocity head h /g Total head, H P/ρ g + /g Significance: Bernoulli s equation is applied in all problems of incompressible fluid flow where energy considerations are involved. But its applications to the following measuring devices are
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22 FLUID MECHANICES LAB:I ) Venturi meter, ) Orifice meter, 3) Pitot tube. Graphs: ) Piezometric head Vs number of tubes ) Total head Vs number of tubes. 3) Velocity head Vs number of tubes. Result: Total head at any section is always constant. Energy level goes on decreasing in the direction of flow. As area decreases pressure head decreases and velocity head increases. Conclusion: As the piezometric head increases the velocity head clearance and as the area increases pressure head i.e. piezometer head also increase from this as the increases from this as the area increases the velocity head decreases.
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24 FLUID MECHANICES LAB:I Experiment:05 Calibration of Venturimeter. Aim: To calibrate venturimeter and to find its coefficient of discharge. Apparatus: Venturimeter fitted across a pipeline leading to a collecting tank, Stop Watch, UTube manometer connected across entry and throat sections etc. Theory: A venturimeter is a device used for measuring the rate of a flow of a fluid flowing through a pipe. It consists of three parts: ) A short converging part, ) Throat and 3) Divergi Figure:  Venturimeter. ng part. On applying the continuity equation &Bernoulli s equation between the two sections, the following relationship is obtained in terms of governing variables. In order to take real flow effect into account, coefficient of discharge ( ) must be determined.pressure tapping is provided at the location before the convergence commences and another pressure tapping is provided at the throat section of a Venturimeter. The Difference in pressure head between the two tapping is measured by means of a Utube manometer. Consider a venturimeter fitted in a horizontal pipe through which a fluid is flowing say water as shown in figure. Let d Diameter at section , P Pressure at section , V Velocity of fluid at section , a Area of cross section at section  Where d, P, V, a are the corresponding values at section . Now applying Bernoulli s equation at section  and , we get As pipe is horizontal Z Z + + But h h () Now applying the continuity equation at sections  and , we get av a V a v V a Now substituting the above value in equation (), we get SRCOE, Lonikand. Civil Engineering Department Page 6
25 FLUID MECHANICES LAB:I Q Q () The equation () gives the discharge under ideal conditions and is called, theoretical discharge. Actual discharge, Q C act d Where Cd is called as Coefficient of venturimeter and its value is less than one. Value of h given by differential Utube manometer: Case I:  Let the differential manometer contains a liquid which is heavier than the liquid flowing through the pipe, when the venturimeter is horizontal. h x Where Sh Specific gravity of the heavier liquid, SO Specific gravity of the liquid flowing through pipe. X Difference of the heavier liquid column in Utube. Case II:  If the differential manometer contains a liquid which is lighter than the liquid flowing through the pipe, when the venturimeter is horizontal. h x Where Sl Specific gravity of lighter liquid in Utube, SO Specific gravity of the liquid flowing through pipe. X Difference of the heavier liquid column in Utube. Case III:  Let the differential manometer contains a liquid which is heavier than the liquid flowing through the pipe, when the venturimeter is inclined. h x Where Sh Specific gravity of the heavier liquid, SO Specific gravity of the liquid flowing through pipe. X Difference of the heavier liquid column in Utube. Case IV:  If the differential manometer contains a liquid which is lighter than the liquid flowing through the pipe, when the venturimeter is inclined. h x Where Sl Specific gravity of lighter liquid in Utube, SO Specific gravity of the liquid flowing through pipe. X Difference of the heavier liquid column in Utube. Experimental SetUp: ) Venturimeter is fitted to a horizontal pipe line to which an inlet valve is fitted. ) Pressure tabs are provided at entrance and throat section and manometer tubes are fitted to the pressure tapes. 3) Measuring tanks, stop watch and scale are used to measure discharge. Procedure. ) Fill the clean water in the sump tank approximately 3/4 of its height. ) Note the pipe diameter ( ) and throat diameter ( ) of Venturimeter. 3) Note the density of manometer liquid i.e. mercury and that of fluid flowing through pipeline i.e. water. SRCOE, Lonikand. Civil Engineering Department Page 7
26 rise 3.6 FLUID MECHANICES LAB:I 4) Start the flow and adjust the control valve in pipeline for maximum discharge. 5) Measure the pressure difference (H) across the Venturimeter by using U tube manometer. 6) Measure flow rate i.e. actual discharge ( ) through Venturimeter by means of collecting tank. 7) Calculate the theoretical discharge ( ) through Venturimeter by using the formula. 8) Decrease the flow rate by adjusting the control valve and repeat the process for at least five times. 9) Determine the coefficient of discharge ( ) for each flow rate and find the mean value of coefficient of discharge ( ) mean. 0) Plot a graph of ( ) on yaxis versus ( ) on x axis. ) Calculate the slope of graph of ( ) versus ( ), it gives the mean value of coefficient of discharge ( ) mean graphically. Precaution: Care should be taken that all entrapped air is removed. So as to prevent bubble formation in manometer tube and the pipe. Observation: Table:05 Sr. Manometric Reading in H No. meters. X of Meters Time taken to Actual Theoretical Coefficient of 0 ( h )cm water level Discharge Discharge in Discharge. T in seconds In 3 sec Calculation: Sample Calculation for First Reading: a) Head of water, H.6 X b) Actual discharge, 3 sec c) Theoretical discharge, meters. 3 sec d) Coefficient of Discharge, 3 sec Significance: ) Venturi meters / Orifice meter provide the widest variety of measurement options in piped systems for liquids, gas, steam, and mixed media of any metering technology. All while offering the highest degree of traceable accuracy. ) They can be used reliably for billing or custody transfer; and they can be used for rectangular or circular metering. In addition, Venturi meters can be oriented in any plane and can measure accurately whether the line fluid is flowing upwards or downwards. Graph: ) Actual discharge Vs venturimeter head. ) Log Vs Log h SRCOE, Lonikand. Civil Engineering Department Page 8
27 FLUID MECHANICES LAB:I Result: Coefficient of discharge ( ) for Venturimeter is found to be a) experimentally b) Graphically as Conclusion: For venturimeter the value of coefficient of discharge is 0.98 and these are the instruments which are used to measure the discharge through the pipes. In our experiments the value of coefficient of discharge is very nearer to the 0.98.
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29 FLUID MECHANICES LAB:I Experiment:06 Transition of Laminar and turbulent flow through pipes. Aim:  To determine the type of flow by using Reynolds Number. Apparatus: ) Reynolds s experimental arrangement, ) Collecting tank, 3) Stop watch, 4) Scale, Theory: Reynolds carried out experiments to decide limiting values of Reynolds number to quantifiably decide whether the flow is laminar, turbulent or transition. The flows can visualize by passing a streak of dye and observing its motion. Laminar Flow: A flow is said to be laminar when the various fluid particles moves in layer with one layer of fluid living smoothly over on adjacent layer. A laminar flow is one in which the fluid particles moves in layers or laminar with one layer sliding over the other. Therefore there is no exchange of fluid particles from one layer to the other and hence no transfer of later of momentum to be adjacent layers. The particles, in the layer having lower velocity, obstruct the fluid particles in the layer with higher velocity. This obstruction force is called viscous resistance or viscosity. The laminar flow is one in which fluid layers glide over each another. It has low velocity and high viscous resistance. Turbulent Flow: There is a continuous transfer of momentum to adjacent layers. Fluid particles occupy different relative position at different places. It is one in which, the particles get thoroughly mixed on (called turbulence). The turbulent flow has higher velocity. The flow in canals, pipes and rivers is usually turbulent flow. Transition Flow: The transition flow has intermediate properties between the laminar and turbulent flow. In laminar the forces should be considered to calculate the friction loss and in the turbulent flow only the internal forces are considered because the effect of viscous force is negligible as compared to internal forces. Reynolds carried out experiments to decide limiting values of Reynolds number to quantifiably decide whether the flow is laminar, turbulent or transition. If the Reynolds number is less than 000, then it is Laminar Flow figure (a),if the Reynolds number is Figure:  Types of flows. between 000 and 4000 then it is Transition Flow figure (b), If the Reynolds number is greater than 4000, then it is Turbulent figure (c). The flow can be visualized by passing a streak of dye and observing its motion. In the laminar, low velocity flow the streak line is only slightly zig  zag. In the turbulent flow, the dye thoroughly mixes up in the flow. Thus passing through a glass pipe and observing the velocity at different mixing stages of the dye is the principle on which Reynolds apparatus is based. Experimental Setup: The apparatus consist of a glass tube with one end having bell mouth entrance connected to water tank. () The tank is of sufficient capacity to store water.
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31 FLUID MECHANICES LAB:I () At the other end of the glass tube a valve is provided. (3) A small container with dye is provided at top of the tank. (5) This small container with dye is connected to the glass tube where the water is flowing. Reynolds Apparatus Procedure:. Fill the sump tank with sufficient clean water by operating inlet valve.. Now fill up with sufficient clean water in dye tank and put a small amount of potassium permagnet in it. 3. Start water flow. 4. Adjust dye water flow to about litres / minute. 5. Start the pump and inject the dye. 6. Wait for some time, a steady line of dye will be observed. 7. Note down the flow rate i.e. 8. Slowly increase the water flow sees that water level in supply tank remains constant. 9. At particular flow rate dye line will be disturbed, note down this flow rate. 0. Further increase the flow. The disturbance of dye line will go on increasing and at certain flow. The dye line diffuses over the entire cross section.. Note down this flow rate.. The whole procedure is repeated for 3 times. Specifications: Diameter of glass tube, d 0.0 meter Area of tank a 4 Area of the tank A 0.3 x Kinematic viscosity for water γ x0 6 sec Observation Table: Sr. Velocity Time required for Discharge Reynolds Observed no. m/sec 0 cm rise of 3 Number flow water. regimes V T Q Re Calculation: Sample Calculation for First Reading: Discharge:
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33 γ FLUID MECHANICES LAB:I Q act Velocity: V Q act meter / Second a Reynold s Number: R e V d Volume of water collected Time required to collect water in a tank for 0 cm Significance: () To predict type of flow in pipes. () To predict type of flow in channels Conclusion. We have studied the use of Reynolds apparatus to finding types of flow such as laminar flow, turbulent flow and transition flow etc. m 3 sec SRCOE, Lonikand. Civil Engineering Department Page
34 0.079 FLUID MECHANICES LAB:I Experiment:07 Minor loss in a pipe system for a given pipe. Aim: To determine minor losses due to pipe fittings such as Expansion, Contraction, Bend, Elbow, etc. Apparatus: A pipe elbow, A sudden contraction pipe, A sudden expansion pipe, A pipe bend, A collecting tank, A stop watch, Scale etc. Theory: When a fluid is flowing (turbulent flow) through a pipe, the fluid experiences some of the energy of fluid is lost. This loss of energy is classified as: ) Major Energy losses: This is due to the friction and it is calculated by the following formulae: a) DarcyWeisbach formula b) Chezy s formula ) Minor Energy losses: This loss of energy is due to change of velocity of the flowing fluid in magnitude or direction. This is due to a) Sudden expansion of pipe, b) Sudden contraction of pipe, c) Bend in pipe, d) Pipe fittings etc, e) At the entrance of pipe, f) At the exit of a pipe. g) An obstruction in pipe. Major Energy losses: DarcyWeisbach formula: 4 Where loss of head due to friction, V mean velocity of fluid, f coefficient of friction which is a function of Reynolds number 6 for < 000, 4 for varying Chezy s Formula: V C from 4000 to Where m hydraulic mean depth, m 4 I loss of head per unit length of pipe, I Chezy s constant.
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36 f FLUID MECHANICES LAB:I Minor Energy losses: This loss of energy is due to change of velocity of the flowing fluid in magnitude or direction. a) Sudden expansion of pipe: Due to sudden change of diameter of the pipe, the liquid flowing from smaller pipe to is not able to follow the abrupt change of the boundary. Thus the flow separates from the boundary and turbulent eddies are formed. The loss of energy takes place due to the formation of these eddies. This is called as loss of energy due to sudden expansion of pipe. Consider a liquid flowing through a pipe which has sudden enlarged form from maller diameter to a larger diameter as shown in figure. Now consider two section  and  before and after the enlargement. Let P pressure intensity at setion  V velocity at section  A area of pipe at section  Where P, V and A are the corresponding values at section, Now applying Bernoulli s theorem to sectio and , h V V he g b) Sudden contraction of pipe: As the liquid flows from larger pipe to smaller pipe, the area of flow goes on decreasing and becomes minimum at section CC as shown in figure. This section CC is called Venacontracta, after section CC a sudden enlargement of the area takes place. The loss of head due to sudden contraction is actually due to sudden enlargement from Venacontracta to smaller pipe. Let Area of flow at section CC VC Velocity of flow at section CC A Area of flow at section  V Velocity of flow at section  hc Loss of head due to sudden contraction. Now, hc Actual loss of head due to enlargement from CC to section  and is given by equation as () From continuity equation, we have A c A C c Now substuting the above value in equation (), SRCOE, Lonikand. Civil Engineering Department Page 4
37 , FLUID MECHANICES LAB:I k where k If the value ofis assumed to be equal to 0.6, then K Then becomes as k If the value of Cc is not given then the head loss due to contraction is taken as, 0.5 c) Bend in Pipe: Where there is any bend in a pipe, the velocity of flow changes, due to which the separation of the flow from the boundary and also formation of eddies, takes place. Thus the energy is lost. Loss of head in pipe due to bend is expressed as, h b Where hb loss of head due to bend, V velocity of flow, K coefficient of bend, The value of k depends on, i) Angle of bend, ii) Radius of curvature of bend, iii) Diameter of pipe. d) Pipe fittings: The loss of head in the various pipe fittings such as valves, couplings etc., hf Where V velocity of flow, k coefficient of pipe fitting. e) An obstruction in pipe: Head loss due to obstruction f) Entrance of a pipe: This is loss of energy which occurs when a liquid enters a pipe which is connected to a large tank or reservoir. This loss is similar to the loss of head due to sudden contraction. This loss depends on the form of entrance. For a sharp edge entrance, this lossis slightly more than a rounded or bell mouthed entrance. In practice the value of loss of head at the entrance of a pipe with sharp cornered entrance is taken as 0.5. g) Exit of pipe: This is the loss of head due to the velocity of liquid at outlet of the pipe which is dissipated either in the form of a free jet or it is lost in the tank or reservoir. This loss is equal to. h) Obstruction in a pipe: Whenever there is an obstruction ina pipe, the loss of energy takes place due to reduction of the area of the crosssection of the pipe at the place where obstruction is present. There is sudden enlargement of the area of flow beyond the obstruction due to which loss of head takes place and is equal to SRCOE, Lonikand. Civil Engineering Department Page 5
38 FLUID MECHANICES LAB:I Experimental SetUp: ) Basic pipe of sufficient length to flow the water, ) Measuring tank, 3) Pipe fittings such as, a) Sudden expansion, b) Sudden contraction, c) Pipe bend, d) Pipe elbow, e) Flow control valve etc. 4) Differential manometer. Procedure:. Collect clean water in the sump tank.. Start the motor, allow the water to flow the pipe fittings like sudden expansion, sudden contraction, bend, elbow. 3. Take the manometric reading. 4. Now find the discharge of water flowing the pipe, by noting time to collect the water for a rise of 0 cm in the tank. 5. The above procedure is repeated for all fittings and readings are entered in the table. Observation: Table:07 Loss of Head due to Sudden Expansion 3.6 Sr.no. Manometric Reading in Discharge meters. X H M m M M 3 sec m Specification: d d Given Given a a Calculation: Sample Calculation for First Reading: H 3.6 Discharge 3 sec m/sec meters m/sec /g meter
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40 .00 FLUID MECHANICES LAB:I Observation: Table:08 Loss of Head due to Sudden Contraction. Sr.no. Manometric Reading 3.6 X H K Discharge Velocity Specification: d d M M M M 3 sec Given Given m a The following value table gives the value of K for the corresponding value of K Calculation: Sample calculation for first reading: For first reading: 3.6 meters H Discharge 3 sec m/sec m/sec K meter Observation: Sr.no. Manometric Reading 3.6 X Table:09 Loss of head due to Bend. H K Discharge m m M M 3 sec m
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42 H Discharge. FLUID MECHANICES LAB:I d d Given a Given The following value table gives the value of K for the corresponding value of K Calculation: Sample calculation for first reading: For first reading: 3.6 H in meters Discharge 3 m/sec sec K meter Observation: Table:0 Loss of head due to Elbow. Sr.no. Manometric Reading 3.6 X K sec M m m m Specifications: d Given d Given M a The following value table gives the value of K for the corresponding value of K Calculation: Sample calculation for first reading: For first reading: 3.6 in meters H 3 sec Discharge m/sec
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44 FLUID MECHANICES LAB:I in m/sec K meter Significance: () For design of pipes in water supply schemes. () For design of sewer pipe schemes. (3) In chemical industry. (4) In dairies. Result. Conclusion. The experiment is conducted using pipe fitting apparatus to determine different losses due to pipe fittings.
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46 FLUID MECHANICES LAB:I Experiment:08 Demonstration of fluid flow through appropriate VCD/Audio visual/ppt.
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48 FLUID MECHANICES LAB:I Assignment No:I Objective: Solving pipe network problem (HardCross method) using Excel work sheet. Problem: Calculate the discharge in each pipe of the network shown in figure. The pipe network consists of five pipes. The head loss h f in a pipe is given by hf rq. The values of r for various QS Q Solution: Loop ABC Pipe Discharge R rq Rq QS AB BC AC Loop BDC Pipe Discharge R rq rq Q BD DC CB Thus applying the above obtained correction the modified discharge for various pipe which is the distribution for second trial. For this distribution the correction Q for the loops ABC and BDC are computed as follows. Loop ABC Pipe Discharge R rq rq AB BC AC Loop BDC Pipe Discharge R rq rq BD DC CB Thus applying the above obtained correction the modified discharges for the various pipe which is the distribution for the third trial. For QS the distribution the correction for loops ABC and BDC are computed as follows: Loop ABC Pipe Discharge R rq rq AB BC 44 4 AC Result:  To solve the problem in excel works sheet and final answer is SRCOE, Lonikand. Civil Engineering Department Page 3
49 FLUID MECHANICES LAB:I or Objective: Three reservoir problem. Problem: Three reservoirs A, B and C are connected by a pipe system as shown in figure. The length and diameters of pipes, and are 800 m, 000 m, 800 m and 300 mm, 00 mm and 50 mm respectively. Determine te piezometric head at junction D. Take f Assignment No:II Objective: Determination of friction factor for a pipe using any programming language Problem: A rough pipe is of diameter 8.0 cm. The velocity at a point 3.0 cm from wall is 30% more than the velocity at a point cm from pipe wall. Determine the average height of the roughness.
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