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CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK 1 R.M.K COLLEGE OF ENGINEERING AND TECHNOLOGY RSM NAGAR, PUDUVOYAL-601206 DEPARTMENT OF MECHANICAL ENGINEERING CE6451 – FLUID MECHANICS & MACHINERY III SEM Regulation 2013
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FLUID MECHANICS

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• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 1

R.M.K COLLEGE OF ENGINEERING

AND TECHNOLOGY RSM NAGAR, PUDUVOYAL-601206

DEPARTMENT OF MECHANICAL ENGINEERING

CE6451 FLUID MECHANICS & MACHINERY

III SEM

Regulation 2013

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 2

UNIT - I - FLUID PROPERTIES AND FLOW CHARACTERISTICS Part A 1.1)What is a fluid? How are fluids classified? 1.2)Define fluid. Give examples. [DEC 10] 1.3)How fluids are classified? [DEC 08, JUN 12] 1.4)Distinguish between solid and fluid. [JUN 06] 1.5)Differentiate between solids and liquids. [JUN 07] 1.6)Discuss the importance of ideal fluid. [MAY 11] 1.7)W h a t is a real fluid? [MAY 03] 1.8)Define Newtonian and Non Newtonian fluids. [DEC 08] 1.9)What are Non Newtonian fluids? Give example. [DEC 09] 1.10)Differentiate between Newtonian and Non Newtonian fluids. [DEC 07] 1.11)What is the difference between an ideal and a real fluid? 1.12)Differentiate between liquids and gases. 1.13)Define Pascals law. [DEC 2005, 2008] 1.14)Define the term density. 1.15)Define mass density and weight density. [DEC 07] 1.16)Distinguish between the mass density and weight density.[JUN 09] 1.17)Define the term specific volume and express its units.[MAY 11] 1.18)Define specific weight. 1.19)Define specific weight and density. [JUN 12] 1.20)Define density and specific gravity of a fluid. [DEC 12] 1.21)Define the term specific gravity. 1.22)What is specific weight and specific gravity of a fluid? [MAY 10] 1.23)What is specific gravity? How is it related to density? [MAY 08] 1.24)What do you mean by the term viscosity? 1.25)What is viscosity? What is the cause of it in liquids and in gases?[DEC 05] 1.26)Define Viscosity and give its unit. [DEC 03] 1.27)Define Newtons law of viscosity. [DEC 12] 1.28)State the Newton's law of viscosity.[MAY, DEC 05, JUN 07] 1.29)Define Newtons law of viscosity and write the relationship between shear stress

and velocity gradient?[DEC 06] 1.30)What is viscosity and give its units? [MAY 11] 1.31)Define coefficient of viscosity. [MAY 05] 1.32)Define coefficient of volume of expansion. [DEC 12] 1.33)Define relative or specific viscosity. [JUN 13] 1.34)Define kinematic viscosity. [DEC 09] 1.35)Define kinematic and dynamic viscosity. [JUN 06] 1.36)Mention the significance of kinematic viscosity. [DEC 11] 1.37)What is dynamic viscosity? What are its units? 1.38)Define dynamic viscosity. [DEC 08, JUN 12] 1.39)Define the terms kinematic viscosity and give its dimensions.[JUN 09] 1.40)What is kinematic viscosity? State its units? [JUN 14] 1.41)Differentiate between kinematic viscosity of liquids and gases with respect to

pressure [DEC 13] 1.42)Write the units and dimensions for kinematic and dynamic viscosity.[DEC 05] 1.43)What are the units and dimensions for kinematic and dynamic viscosity of a

fluid? [DEC 06, 12]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 3

1.44)Differentiate between kinematic and dynamic viscosity.[JUN 07, DEC 08, 11] 1.45)How does the dynamic viscosity of liquids and gases vary with

temperature?[DEC 07, MAY 08] 1.46)What are the variations of viscosity with temperature for fluids? [DEC 09] 1.47)What is the effect of temperature on viscosity of water and that of air? 1.48)Why is it necessary in winter to use lighter oil for automobiles than in summer?

To what property does the term lighter refer? [DEC 10] 1.49)Define the term pressure. What are its units? [DEC 05] 1.50)Give the dimensions of the following physical quantities[MAY 03]

a) Pressure b) surface tension c) Dynamic viscosity d) kinematic

1.51)Define eddy viscosity. How it differs from molecular viscosity?[DEC 10] 1.52)Define surface tension. [JUN 06] 1.53)Define surface tension and expression its unit. [MAY 11] 1.54)Define capillarity. [DEC 05, JUN 06] 1.55)What is the difference between cohesion and adhesion? 1.56)Define the term vapour pressure. 1.57)What is meant by vapour pressure of a fluid? [MAY 10] 1.58)What are the types of pressure measuring devices? 1.59)What do you understand by terms: (i) Isothermal process ii) adiabatic process 1.60)What do you mean by capillarity? [DEC 09] 1.61)Explain the phenomenon of capillarity. 1.62)What is compressibility of fluid? 1.63)Define compressibility of the fluid.[DEC 2008, JUN 09] 1.64)Define compressibility and viscosity of a fluid. [MAY 05] 1.65)Define coefficient of compressibility. What is its value for ideal gases? [DEC 10] 1.66)List the components of total head in a steady, incompressible irrotational

flow.[DEC 09] 1.67)Define the bulk modulus of fluid. [DEC 08] 1.68)Define - compressibility and bulk modulus. [DEC 2011] 1.69)Write short notes on thixotropic fluid. 1.70)What is Thixotropic fluid? [DEC 03] 1.71)One poises equal toPa.s. 1.72)Give the types of fluid flow. 1.73)Define steady flow and give an example. 1.74)Define unsteady flow and give an example. 1.75)Differentiate between the steady and unsteady flow. [JUN 06] 1.76)When the flow regarded as unsteady? Give an example for unsteady flow.

MAY03 1.77)Define uniform flow and give an example. 1.78)Define non uniform flow and give an example. 1.79)Differentiate between steady flow and uniform flow.[DEC 07] 1.80)Define laminar and turbulent flow and give an example. 1.81)Differentiate between laminar and turbulent flow.[DEC 2005, 2008] 1.82)Distinguish between Laminar and Turbulent flow. [MAY 10] [DEC 06] 1.83)State the criteria for laminar flow. [DEC 08] 1.84)State the characteristics of laminar flow. [MAY 10]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 4

1.85)What are the characteristics of laminar flow? [JUN 14] 1.86)Mention the general characteristics of laminar flow. [JUN 13] 1.87)Define compressible and incompressible flow and give an example. 1.88)Define rotational and irrotational flow and give an example. 1.89)Distinguish between rotation and circularity in fluid flow. [MAY 05] 1.90)Define stream line. What do stream lines indicate? [DEC 07] 1.91)Define streamline and path line in fluid flow. [DEC 05] 1.92)What is stream line and path line in fluid flow? [MAY 10] 1.93)What is a streamline? [DEC 10] 1.94)Define streak line. [MAY 08] 1.95)Define stream function. [MAY 2010, JUN 12] 1.96)Define control volume. 1.97)What is meant by continuum? [DEC 08] 1.98)Define continuity equation. 1.99)Write down the equation of continuity. [DEC 2008, 2009, 2012] 1.100)State the continuity equation in one dimensional form?[JUN12] 1.101)State the general continuity equation for a 3 - D incompressible fluid flow. [JUN

07, DEC 12] 1.102)State the continuity equation for the case of a general 3-D flow. [DEC 07] 1.103)State the equation of continuity in 3dimensional incompressible flow. [DEC 05] 1.104)State the assumptions made in deriving continuity equation[DEC 11] 1.105)Define Euler's equation of motion. 1.106)Write the Euler's equation. [MAY 11] 1.107)What is Eulers equation of motion? [DEC 08] 1.108)Define Bernoulli's equation. 1.109)Write the Bernoullis equation in terms of head. Explain each term. [DEC07] 1.110)What are the basic assumptions made is deriving Bernoullis theorem?[DEC

05,12] 1.111)List the assumptions which are made while deriving Bernoullis

equation.[JUN12] 1.112)State at least two assumptions of Bernoullis equation. [JUN 09] 1.113)What are the three major assumptions made in the derivation of the Bernoullis

equation? [MAY 08] 1.114)State Bernoullis theorem as applicable to fluid flow. [DEC 03] 1.115)Give the assumptions made in deriving Bernoullis equation.[DEC 12] 1.116)What are the applications of Bernoullis theorem?[MAY 10] 1.117)Give the application of Bernoullis equation. 1.118)List the types of flow measuring devices fitted in a pipe flow, which uses the

principle of Bernoullis equation. [JUN 12] 1.119)Mention the uses of manometer.[DEC 09] 1.120)State the use of venturimeter.[JUN 06] 1.121)Define momentum principle. 1.122)Define impulse momentum equation. 1.123)Write the impulse momentum equation. [JUN 07] 1.124)What do you understand by impulse momentum equation [JUN 13] 1.125)State the momentum equation. When can it applied.[JUN 09] 1.126)State the usefulness of momentum equation as applicable to fluid flow

phenomenon.[JUN 2007, DEC 12]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 5

1.127)Define discharge (or) rate of flow. 1.128)Discuss the momentum flux. [MAY 11] 1.129)Find continuity equation, when the fluid is incompressible and Densities are

equal 1.130)What is the moment of momentum equation? [JUN 14] 1.131)Explain classification of fluids based on viscosity. 1.132)State and prove Euler's equation of motion. Obtain Bernoulli's equation from

Euler's equation. 1.133)State and prove Bernoulli's equation. What are the limitations of The Bernoulli's

equation? 1.134)State the momentum equation. How will you apply momentum equation for

determining the force exerted by a flowing liquid on a pipe bend? 1.135)Give the equation of continuity. Obtain an expression for continuity equation for

a three - dimensional flow. 1.136)Calculate the density of one litre petrol of specific gravity 0.7?[MAY 11] 1.137)A soap bubble is formed when the inside pressure is 5 N/m2 above the

atmospheric pressure. If surface tension in the soap bubble is 0.0125 N/m, find the diameter of the bubble formed.[MAY 10]

1.138)The converging pipe with inlet and outlet diameters of 200 mm and 150 mm carries the oil whose specific gravity is 0.8.The velocity of oil at the entry is 2.5 m/s, find the velocity at the exit of the pipe and oil flow rate in kg/sec. [MAY 10]

1.139)Find the height through which the water rises by the capillary action in a 2mm bore if the surface tension at the prevailing temperature is0.075 g/cm.[MAY 03]

1.140)Find the height of a mountain where the atmospheric pressure is 730mm of Hg at normal conditions.[DEC09]

1.141)Suppose the small air bubbles in a glass of tap water MAY be on the order of 50 m in diameter. What is the pressure inside these bubbles? [DEC 10]

1.142)An open tank contains water up to depth of 2.85m and above it an oil of specific gravity 0.92 for the depth of 2.1m. Calculate the pressures at the interface of two liquids and at the bottom of the tank. [MAY 11]

1.143)Two horizontal plates are placed 12.5mm apart, the space between them is being filled with oil of viscosity 14 poise. Calculate the shear stress in the oil if the upper plate is moved with the velocity of 2.5m/s. Define specific weight.[JUN 12]

1.144)Calculate the height of capillary rise for water in a glass tube of Diameter 1mm.[JUN 12]

PART B 1.145)What are the various classification of fluids? Discuss [DEC 12] 1.146)State and prove Pascal's law. [JUN, DEC 07] 1.147)What is Hydrostatic law? Derive an expression to show the same.[DEC 09] 1.148)Explain the properties of hydraulic fluid. [DEC 09] 1.149)Discuss the equation of continuity. Obtain an expression for continuity equation in three dimensional forms.[MAY 11] 1.150)Explain in detail the Newton's law of viscosity. Briefly classify the fluids based on the density and viscosity. Give the limitations of applicability of Newton's law of viscosity.[MAY 11] 1.151)State the effect of temperature and pressure on viscosity. [JUN 09] 1.152)Explain the term specific gravity, density, compressibility and vapour pressure.

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 6

[JUN 09] 1.153)Explain the terms Specific weight, Density, Absolute pressure and Gauge pressure.[MAY 11] 1.154)Define Surface tension and also compressibility of a fluid?[DEC 06] 1.155)Explain the phenomenon surface tension and capillarity. [MAY 11] 1.156)Derive an expression for the capillary rise of a liquid having surface tension and contact angle between two vertical parallel plates at a distance W apart. If the plates are of glass, what will be the capillary rise of water? Assume = 0.773N / m, = 0 Take W=l mm.[JUN 14] 1.157)What is compressibility of fluids? Give the relationship between compressibility and bulk modulus[DEC09] 1.158)Prove that the relationship between surface tension and pressure inside the droplet of liquid in excess of outside pressure is given by P = 4/d.[MAY10,11,DEC08] 1.159)Explain the following 1. Capillarity 2. Surface tension 3. Compressibility 4. Kinematic viscosity [JUN12] 1.160)Derive the energy equation and state the assumptions made while deriving the equation.[DEC 10] 1.161)Derive Euler's equation of motion.[JUN 14] 1.162)Derive from the first principles, the Eulers equation of motion for a steady flow along a stream line. Hence derive Bernoulli equation. State the various assumptions involved in the above derivation.[JUN 09] 1.163)Derive from basic principle the Eulers equation of motion in 2D flow in X-Y coordinate system and reduce the equation to get Bernoullis equation for unidirectional stream lined flow.[MAY 05] 1.164)State Eulers equation of motion, in the differential form. Derive Bernoullis equation from the above for the cases of an ideal fluid flow.[JUN 07, DEC 12] 1.165)State the law of conservation of man and derive the equation of continuity in Cartesian coordinates for an incompressible fluid. Would it alter if the flow were unsteady, highly viscous and compressible?[MAY 11] 1.166)Derive the equation of continuity for one dimensional flow.[DEC 08, MAY10] 1.167)Derive the continuity equation for 3 dimensional flow in Cartesian coordinates.[JUN 06] 1.168)Derive the general form of continuity equation in Cartesian coordinates. [DEC 12] 1.169)Derive the continuity equation of differential form. Discuss weathers equation is valid for a steady flow or unsteady flow, viscous or in viscid flow, compressible or incompressible flow. [MAY 03] 1.170)Derive continuity equation from basic principles.[DEC 09] 1.171)Derive Bernoullis equation along with assumptions made.[JUN 07] 1.172)State Bernoullis theorem for steady flow of an in compressible fluid. [DEC 04, 05, MAY 10, JUN 13] 1.173)State Bernoullis theorem for steady flow of an in compressible fluid. 1.174)Derive an expression for Bernoulli equation and state the assumptions made.[JUN 09] 1.175)State the assumptions in the derivation of Bernoullis equation.[JUN, DEC 07] 1.176)Derive an expression for Bernoullis equation for a fluid flow.[DEC 04, 05, MAY 10] 1.177)Derive Bernoullis equation from the first principles? State the assumptions made while deriving Bernoullis equation.[JUN 12]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 7

1.178)Derive from basic principle the Eulers equation of motion in Cartesian co -ordinates system and deduce the equation to Bernoullis theorem steady irrotational flow.[MAY 04] 1.179)Derive the Eulers equation of motion and deduce the expression to Bernoullis equation.[DEC 12] 1.180)Develop the Euler equation of motion and then derive the one dimensional form of Bernoullis equation.[DEC 11] 1.181)Show that for a perfect gas the bulk modulus of elasticity equals its pressure for 1. An isothermal process 2. times the pressure for an isentropic process[MAY 03] 1.182)State and derive impulse momentum equation. [MAY 05] 1.183)Derive momentum equation for a steady flow. [JUN 12] 1.184)Derive the linear momentum equation using the control volume approach and determine the force exerted by the fluid flowing through a pipe bend. [DEC 11] 1.185)With a neat sketch, explain briefly an orifice meter and obtain an expression for the discharge through it.[DEC 12] 1.186)Draw the sectional view of Pitots tube and write its concept to measure velocity of fluid flow? [MAY 05]

PROBLEMS 1.187)A soap bubble is 60mm in diameter. If the surface tension of the soap film is 0.012 N/m. Find the excess pressure inside the bubble and also derive the expression used in this problem.[DEC 09] 1.188)A spherical water droplet of 5 mm in diameter splits up in the air into 16 smaller droplets of equal size. Find the work involved in splitting up the droplet. The surface tension of water MAY be assumed as 0.072 N/m [DEC 12] 1.189)A liquid weighs 7.25N per litre. Calculate the specific weight, density and specific gravity of the liquid. 1.190)One litre of crude oil weighs 9.6N. Calculate its specific weight, density and specific gravity.[DEC 08] 1.191)Determine the viscosity of a liquid having a kinematic viscosity 6 stokes and specific gravity 1.9.[DEC 08, MAY 10] 1.192)Determine the mass density; specific volume and specific weight of liquid whose specific gravity 0.85.[MAY 10] 1.193)If the volume of a balloon is to reach a sphere of 8m diameter at an altitude where the pressure is 0.2 bar and temperature -40C. Determine the mass hydrogen to be charged into the balloon and volume and diameter at ground level. Where the pressure is 1bar and temperature is 25C. [DEC 09] 1.194)A pipe of 30 cm diameter carrying 0.25 m3/s water. The pipe is bent by 135 from the horizontal anti-clockwise. The pressure of water flowing through the pipe is 400 kN. Find the magnitude and direction of the resultant force on the bend. [DEC 11] 1.195)A liquid has a specific gravity of 0.72. Find its density and specific weight.

Find also the weight per litre of the liquid. 1.196)A 1.9mm diameter tube is inserted into an unknown liquid whose density is 960kg/m3, and it is observed that the liquid raise 5mm in the tube, making a contact angle of 15. Determine the surface tension of the liquid.[MAY 08] 1.197)A 0.3m diameter pipe carrying oil at 1.5m/s velocity suddenly expands to 0.6m diameter pipe. Determine the discharge and velocity in 0.6m diameter pipe.[JUN12] 1.198)Explain surface tension. Water at 20C ( = 0.0.73N/m, = 9.8kN/m3 and angle of contact = 0) rises through a tube due to capillary action. Find the tube diameter requires, if the capillary rise is less than 1mm.[DEC 10]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 8

1.199)A Newtonian fluid is filled in the clearance between a shaft and a concentric sleeve. The sleeve attains a speed of 50cm/s, when a force of 40N is applied to the sleeve parallel to the shaft. Determine the speed of the shaft, if a force of 200N is applied.[DEC 06] 1.200)An oil film thickness 10mm is used for lubrication between the square parallel plate of size 0.9 m * 0.9 m, in which the upper plate moves at 2m/s requires a force of 100 N to maintain this speed. Determine the

Dynamic viscosity of the oil in poise and Kinematic viscosity of the oil in stokes. The specific gravity of the oil is 0.95.[DEC 2003]

1.201)The space between two square flat parallel plates is filled with oil. Each side of the plate is 60cm. The thickness of the oil film is 12.5mm. The upper plate, which moves at 2.5 meter per sec, requires a force of 98.1N to maintain the speed. Determine the 1. Dynamic viscosity of the oil in poise and 2. Kinematic viscosity of the oil in stokes.

3. The specific gravity of the oil is 0.95. [DEC 12] 1.202)What is the bulk modulus of elasticity of a liquid which is compressed in a cylinder from a volume of 0.0125m3 at 80N/cm2 pressure to a volume of 0.0124m3 at pressure 150N/cm2 [DEC 04] 1.203)Determine the bulk modulus of elasticity of elasticity of a liquid, if the pressure of the liquid is increased from 7MN/m2 to 13MN/m2, the volume of liquid Decreases by 0.15%.[JUN 09] 1.204)The measuring instruments fitted inside an airplane indicate the pressure 1.032 *105Pa, temperature T0 = 288 K and density 0 = 1.285 kg/m3 at takeoff. If a standard temperature lapse rate of 0.0065 K/m is assumed, at what elevation is the plane when a pressure of 0.53*105 recorded? Neglect the variations of acceleration due gravity with the altitude and take airport elevation as 600m. A person must breathe a constant mass rate of air to maintain his metabolic process. If he inhales 20 times per minute at the airport level of 600m, what would you except his breathing rate at the calculated altitude of the plane? [JUN 09] 1.205)The space between two square parallel plates is filled with oil. Each side of the plate is 75 cm. The thickness of oil film is 10 mm. The upper plate which moves at 3 m/s requires a force of 100 N to maintain the speed. Determine the

Dynamic viscosity of the oil Kinematic viscosity of the oil, if the specific gravity of the oil is 0.9.

1.206)A rectangular plate of size 25cm* 50cm and weighing at 245.3 N slides down at 30 inclined surface with uniform velocity of 2m/s. If the uniform 2mm gap between the plates is inclined surface filled with oil. Determine the viscosity of the oil. [MAY 2004, DEC 12] 1.207)A space between two parallel plates 5mm apart, is filled with crude oil of specific gravity 0.9. A force of 2N is require to drag the upper plate at a constant velocity of 0.8m/s. the lower plate is stationary. The area of upper plate is 0.09m2. Determine the dynamic viscosity in poise and kinematic viscosity of oil in strokes. [JUN 09]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 9

1.208)The space between two large flat and parallel walls 25mm apart is filled with liquid of absolute viscosity 0.7 Pa.sec. Within this space a thin flat plate 250mm * 250 mm is towed at a velocity of 150mm/s at a distance of 6mm from one wall, the plate and its movement being parallel to the walls. Assuming linear variations of velocity between the plates and the walls, determine the force exerted by the liquid on the plate.[JUN 12] 1.209)A jet issuing at a velocity of 25 m/s is directed at 35 to the horizontal. Calculate the height cleared by the jet at 28 m from the discharge location? Also determine the maximum height the jet will clear and the corresponding horizontal location. [DEC 11] 1.210)A flat plate of area 0.125m2 is pulled at 0.25 m/sec with respect to another parallel plate 1mm distant from it, the space between the plates containing water of viscosity 0.001Ns/ m2. Find the force necessary to maintain this velocity. Find also the power required. 1.211)Lateral stability of a long shaft 150 mm in diameter is obtained by means of a 250 mm stationary bearing having an internal diameter of 150.25 mm. If the space between bearing and shaft is filled with a lubricant having a viscosity 0.245 N s/m2, what power will be required to overcome the viscous resistance when the shaft is rotated at a constant rate of 180 rpm? [DEC 10] 1.212)Find the kinematic viscosity of water whose specific gravity is 0.95 and Viscosity is 0.0011Ns/m2. 1.213)The dynamic viscosity of oil, used for lubrication between a shaft and sleeve is6poise. The shaft is of diameter 0.4m and rotates at 190 rpm. Calculate the power lost in the bearing for a sleeve length of 90mm. The thickness of the oil film is 1.5mm.[DEC 07, JUN 12] 1.214)A 200 mm diameter shaft slides through a sleeve, 200.5 mm in diameter and 400 mm long, at a velocity of 30 cm/s. The viscosity of the oil filling the annular space is m = 0.1125 NS/ m2. Find resistance to the motion. [A.U. DEC 08] 1.215)A 0.5m shaft rotates in a sleeve under lubrication with viscosity 5 Poise at 200rpm. Calculate the power lost for a length of 100mm if the thickness of the oil is 1mm. [DEC 09] 1.216)A 15 cm diameter vertical cylinder rotates concentrically inside another cylinder of diameter 15.10 cm. Both cylinders are 25 cm high. The space between the cylinders is filled with a liquid whose viscosity is unknown. If a torque of 12.0 Nm is required to rotate the inner cylinder at 100 rpm, determine the viscosity of the fluid. [JUN 13] 1.217)A400 mm diameter shaft is rotating at 200 r.p.m. in a bearing of length 120 mm. If the thickness of film is 1.5 mm and the dynamic viscosity of the oil is 0.7 N.s/m2, determine (i) Torque required to overcome friction in bearing (ii) Power utilized to overcoming viscous friction. Assume linear velocity profile.[JUN 14] 1.218)Calculate the gauge pressure and absolute pressure within (i) a droplet of water 0.4cm in diameter (ii) a jet of water 0.4cm in diameter. Assume the surface tension of water as 0.03N/m and the atmospheric pressure as 101.3kN/m2. 1.219)What do you mean by surface tension? If the pressure difference between the inside and outside of air bubble of diameter, 0.01 mm is 29.2kPa, what will be the surface tension at air water interface? Derive an expression for the surface tension in

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 10

the air bubble and from it, deduce the result for the given conditions. [DEC 05] 1.220)At the depth of 2km in ocean the pressure is 82401kN/m2. Assume the specific gravity at the surface as 10055 N/m3 and the average bulk modulus of elasticity is 2.354 * 109 N/m2 for the pressure range. Determine the change in specific volume between the surface and 2km depth and also determine the specific weight at the depth?[MAY 04, DEC 12] 1.221)At the depth of 8km from the surface of the ocean, the pressure is stated to be 82MN/m2. Determine the mass density, weight density and specific volume of water at this depth. Take density at the surface = 1025kg/m3 and bulk modulus K = 2350MPa for indicated pressure range.[JUN 09] 1.222)Eight kilometers below the surface of ocean pressure is 81.75MPa. Determine the density of sea water at this depth if the density at the surface is 1025 kg/m3 and the average bulk modulus of elasticity is 2.34GPa. [JUN 12] 1.223)A liquid is compressed in a cylinder having a volume of 0.012 m3 at a pressure of 690 N/cm2. What should be the new pressure in order to make its volume 0.0119 m3? Assume bulk modulus of elasticity (K) for the liquid = 6.9 x 104 N/cm2. [JUN 13] 1.224)Calculate the capillary rise in glass tube of 3 mm diameter when immersed in mercury; take the surface tension and the angle of contact of mercury as 0.52 N/m and 130 respectively. Also determine the minimum size of the glass tube, if it is immersed in water, given that the surface tension of water is 0.0725 N/m and capillary rise in the tube is not to exceed 0.5mm.[DEC 03] 1.225)The capillary rise in a glass tube is not to exceed 0.2mm of water. Determine its minimum size, given that the surface tension for water in contact with air = 0.0725N/m.[DEC07, JUN 12] 1.226)Calculate the capillary effect in millimeters in a glass tube of 4mm diameter when immersed in (i) water and (ii) mercury. The temperature of the liquid is 20C and the values of surface tension of water and mercury at 20C in contact with air are 0.0735N/m and 0.51N/m respectively. The contact angle for water u=0 and for mercury u=130.Take specific weight of water at 20C as equal to 9780 N/m3.[DEC 07] 1.227)Derive an expression for the capillary rise at a liquid in a capillary tube of radius r having surface tension and contact angle . If the plates are of glass, what will be the capillary rise of water having = 0.073 N/m, = 0? Take r = 1mm. [DEC 11] 1.228)A pipe containing water at 180kN/m2 pressure is connected to differential gauge to another pipe 1.6m lower than the first pipe and containing water at high pressure. If the difference in height of 2 mercury columns of the gauge is equal to 90mm, what is the pressure in the lower pipe? [DEC 08] 1.229)Determine the minimum size of glass tubing that can be used to measure water level. If the capillary rise in the tube is not exceed 2.5mm. Assume surface tension of water in contact with air as 0.0746 N/m. [DEC 2004, 2012] 1.230)Calculate the capillary effect in millimeters in a glass tube of 4 mm diameter, when immersed in (i) water and (ii) mercury. The temperature of the liquid is 20C and the values of surface tension of water and mercury at 20C in contact with air are

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 11

0.0735 N/m and 0.51 N/m respectively. The contact angle for water u = 0 and for mercury u = 130. Take specific weight of water at 20C as equal to 9790N/ m3. [DEC 05, 07] 1.231)A Capillary tube having inside diameter 6 mm is dipped in CCl4at 20o C. Find the rise of CCl4 in the tube if surface tension is 2.67 N/m and Specific gravity is1.594 and contact angle u is 60 and specific weight of water at 20 C is 9981 N/m3.[DEC 08] 1.232)Two pipes A & B are connected to a U tube manometer containing mercury of density 13,600kg/m3. Pipe A carries a liquid of density 1250kg/m3 and a liquid of density 800kg/m3 flows through a pipe B, The center of pipe A is 80mm above the pipe B. The difference of mercury level manometer is 200mm and the mercury surface on pipe a side is 100mm below the center. Find the difference of pressure between the two connected points of the pipes. [DEC 10] 1.233)A crude oil of viscosity 0.9 poise and relative density 0.9 is flowing through a horizontal circular pipe of diameter 120 mm and length 12 m. Calculate the difference of pressure at the two ends of the pipe, if 785 N of the oils collected in a tank in 25 seconds. [JUN 14] 1.234)A simple U tube manometer containing mercury is connected to a pipe in which a fluid of specific gravity 0.8 and having vacuum pressure is flowing. The other end of the manometer is open to atmosphere. Find the vacuum pressure in the pipe, if the difference of mercury level in the two limbs is 40cm and the height of the fluid in the left from the center pipe is 15cm below. Draw the sketch for the above problem. [MAY 11, JUN 12] 1.235)A U-tube is made of two capillaries of diameter 1.0 mm and 1.5 mm respectively. The tube is kept vertically and partially filled with water of surface tension 0.0736 N/m and zero contact angles. Calculate the difference in the levels of the menisci caused by the capillary.[DEC 10] 1.236)Define the terms gauge pressure and absolute pressure. A U tube containing mercury has its right limb open to atmosphere. The left limb is full of water and is connected to a pipe containing water under pressure, the Centre of which is in the level with the free surface of mercury. If the difference in the levels of mercury in the limbs id 5.1cm, calculate the water pressure in the pipe. [DEC 12] 1.237)The barometric pressure at sea level is 760 mm of mercury while that on a mountain top is735 mm. If the density of air is assumed constant at 1.2 kg/m3, what is the elevation of the mountain top? [DEC 07] 1.238)The barometric pressure at the top and bottom of a mountain are 734mm and 760mm of mercury respectively. Assuming that the average density of air = 1.15kg/m3, calculate the height of the mountain. [DEC 09] 1.239)The maximum blood pressure in the upper arm of a healthy person is about 120 mmHg. If a vertical tube open to the atmosphere is connected to the vein in the arm of the person, determine how high the blood will rise in the tube.Take the density of the blood to be 1050 kg/ m3.[MAY 08] 1.240)When a pressure of 20.7 MN/m2 is applied to 100 L of a liquid, its volume decreases by one L. Find bulk modulus of the liquid and identify this liquid. [DEC 07] 1.241)Determine the minimum size of the glass tubing that can be used to measure

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 12

water level. If the capillary rise in the tube is not to exceed 2.5mm. Assume surface tension of water in contact with air as 0.0746 N/m[MAY 04] 1.242)A cylinder of 0.6m3 in volume contains air at 50oC and 0.3N/mm2 absolute pressure. The air is compressed to 0.3m3. Find the (i) pressure inside the cylinder assuming isothermal process and (ii) pressure and temperature assuming adiabatic process. Take k = 1.4. 1.243)A 30cm dia pipe, conveying water branches into two pipes of diameters 20cm and 15cm respectively. If the average velocity in the 30cm diameter pipe is 2.5m/sec, find the discharge in this pipe. Also determine the velocity in the 15cm diameter pipe if the average velocity in the 20cm diameter pipe is 2m/sec. [DEC 08,MAY 10] 1.244)Water flows through a pipe AB 1.2m diameter at 3m/second then passes through a pipe BC 1.5m diameter. At C, the pipe branches. Branch CD is 0.8m in diameter and carries one - third of the flow in AB. The flow velocity in branch CE is 2.5m/sec. Find the volume rate of flow in AB, the velocity in BC, the velocity in CD and the diameter of CE. 1.245)Water is flowing through a pipe having diameters 20cm and 10cm at sections 1 and 2 respectively. The rate of flow, through the pipe is 35litre/sec. The section 1 is 6m above datum and section 2 is 4m above datum. If the pressure at section 1 is 39.24N/cm2, find the intensity of pressure at section 2. [DEC 08] 1.246)A pipe of diameter 400mm carries water at a velocity of 25m/sec. The pressures at the points A and B are given as 29.43N/cm2 and 22.563 N/cm2 respectively, while the datum head at A and B are 28m and 30m. Find the loss of head between A and B. 1.247)A drainage pipe is tapered in a section running with full of water.The pipe diameters at the inlet and exit are 1000 mm and 50 mm respectively. The water surface is 2 m above the center of the inlet and exit is 3 m above the free surface of the water. The pressure at the exit is250 mm of Hg vacuum. The friction loss between the inlet and exit of the pipe is 1/10 of the velocity head at the exit. Determine the discharge through the pipe.[MAY 10] 1.248)A pipeline 60 cm in diameter bifurcates at a Y- junction into two branches 40 cm and 30 cm in diameter. If the rate of flow in the main pipe is 1.5 m3/s, and the mean velocity of flow in the 30 cm pipe is 7.5 m/s, determine the rate of flow in the 40 cm pipe.[DEC 10] 1.249)A pipeline of 175 mm diameter branches into two pipes which delivers the water at atmospheric pressure. The diameter of the branch 1 which is at 35 counter-clockwise to the pipe axis is 75mm. and the velocity at outlet is 15 m/s. The branch 2 is at 15 with the pipe center line in the clockwise direction has a diameter of 100 mm. The outlet velocity is 15 m/s. The pipes lie in a horizontal plane. Determine the magnitude and direction of the forces on the pipes. [DEC 11] 1.250)A pipeline conveys 10 lit/s of water from an overhead tank to a building. The pipe is 2km long and 15cm diameter, the friction factor is 0.03. It is planned to increase the discharge by 30% by installing another pipeline in parallel with this over half the length. Find the suitable diameter of pipe to be installed. Is there any upper limit on discharge augmentation by this arrangement?[DEC 12] 1.251)The water is flowing through a taper pipe of length 100 m having diameters 600 mm at the upper end and 300 mm at the lower end, at the rate of 50 litres/s. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 13

higher level is 19.62 N/cm2.[JUN 13] 1.252)A 45 reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being 600mm and 300mm respectively. Find the force exerted by water on the bend if the intensity of pressure at the inlet to the bend is 8.829N/cm2 and rate of flow of water is600 litre / sec. 1.253)Gasoline (specific gravity = 0.8) is flowing upwards through a vertical pipe line which tapers from300mm to 150mm diameter.A gasoline mercury differential manometer is connected between 300 mm and 150 mm pipe sections to measure the rate of flow. The distance between the manometer tappings is 1meter and the gauge heading is 500 mm of mercury. Find the (i) differential gauge reading in terms of gasoline head (ii) rate of flow. Assume frictional and other losses are negligible.[JUN 2007, 2014, DEC 12] 1.254)Water enters a reducing pipe horizontally and comes out vertically in the downward direction. If the inlet velocity is 5 m/s and pressure is 80 kPa (gauge) and the diameters at the entrance and exit sections are 30 cm and 20 cm respectively, calculate the components of the reaction acting on the pipe. [JUN 07, DEC 12] 1.255)A horizontal pipe has an abrupt expansion from 10 cm to 16 cm. The water velocity in the smaller section is 12 m/s, and the flow is turbulent. The pressure in the smaller section is 300 kPa. Determine the downstream pressure, and estimate the error that would have occurred if Bernoullis equation had been used. [DEC 11] 1.256)Air flows through a pipe at a rate of 20 L/s. The pipe consists of two sections of diameters20 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Neglecting frictional effects, determine the differential height of water between the two pipe sections. Take the air density to be 1.20 kg/m3.[MAY 08]

1.257)A horizontal venturimeter with inlet diameter 200 mm and throat diameter 100 mm is employed to measure the flow of water.The reading of the differential manometer connected to the inlet is 180 mm of mercury. If Cd = 0.98, determine the rate of flow. [MAY 10] 1.258)A horizontal venturimeter of specification 200mm * 100mm is used to measure the discharge of an oil of specific gravity 0.8. A mercury manometer is used for the purpose. If the discharge is 100 litres per second and the coefficient of discharge of meter is 0.98, find the manometer deflection. [JUN 07] 1.259)Determine the pressure difference between inlet and throat of a vertical venturimeter of size 150 mm x 75 mm carrying oil of S = 0.8 at flow rate of 40 lps. The throat is 150 mm above the inlet. 1.260)A pipe of 300 mm diameter inclined at 30 to the horizontal is carrying gasoline (specific gravity = 0.82). A venturimeter is fitted in the pipe to find out the flow rate whose throat diameter is 150 mm. The throat is 1.2 m from the entrance along its length. The pressure gauges fitted to the venturimeter read 140 kN/m2and

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 14

8 0 k N /m2respectively. Find o u t t h e c o -efficient o f d i s c h a r g e o f venturimeter if the flow is 0.20 m3/s. [MAY 10] 1.261)A venturimeter of throat diameter 0.085m is fitted in a 0.17m diameter vertical pipe in which liquid a relative density 0.85 flows downwards. Pressure gauges ate fitted at the inlet and to the throat sections. The throat being 0.9m below the inlet. Taking the coefficient of the meter as 0.95 find the discharge when the pressure gauges read the same and also when the inlet gauge reads 15000N/m2 higher than the throat gauge. [MAY 11] 1.262)A Venturimeter having inlet and throat diameters 30 cm and 15 cm is fitted in a horizontal diesel pipe line (Sp. Gr. = 0.92) to measure the discharge through the pipe. The venturimeter is connected to a mercury manometer. It was found that the discharge is 8 litres /sec. Find the reading of mercury manometer head in cm. Take Cd =0.96.[DEC 11] 1.263)A venturimeter is inclined at 60 to the vertical and its 150 mm diameter throat is 1.2 m from the entrance along its length. It is fitted to a pipe of diameter 300 mm. The pipe conveys gasoline of S = 0.82 and flowing at 0.215 m3/s upwards. Pressure gauges inserted at entrance and throat show the pressures of 0.141 N/mm2and 0.077 N/mm2respectively. Determine the co-efficient of discharge of the venturimeter. Also determine the reading in mm of differential mercury column, if instead of pressure gauges the entrance and the throat of the venturimeter are connected to the limbs of a U tube mercury manometer.[MAY 04] 1.264)A horizontal venturimeter with inlet and throat diameter 300mm and 100mm respectively is used to measure the flow of water. The pressure intensity at inlet is 130 kN/m2 while the vacuum pressure head at throat is 350 mm of mercury. Assuming 3% head lost between the inlet and throat. Find the value of coefficient of discharge for venturimeter and also determine the rate of flow. [DEC 04, 05, MAY 10] 1.265)A vertical venturimeter carries a liquid of relative density 0.8 and has inlet throat diameters of 150mm and 75mm. The pressure connection at the throat is 150mm above the inlet. If the actual rate of flow is 40litres/sec and Cd = 0.96, find the pressure difference between inlet and throat in N/m2.[JUN 06] 1.266)A 300 mm x 150 mm venturimeter is provided in a vertical pipeline carrying oil of relative density 0.9, the flow being upwards. The differential U tube mercury manometer shows a gauge deflection of 250 mm. Calculate the discharge of oil, if the co-efficient of meter is 0.98.[DEC 07] 1.267)In a vertical pipe conveying oil of specific gravity 0.8, two pressure gauges have been installed at A and B, where the diameters are 160mm a 80mm respectively. A is 2m above B. The pressure gauge readings have shown that the pressure at B is greater than at A by 0.981 N/cm2. Neglecting all losses, calculate the flow rate. If the gauges at A and B are replaced by tubes filled with the same liquid and connected to a U tube containing mercury, calculate the difference in the level of mercury in the two limbs of the U tube.[JUN12] 1.268)Determine the flow rate of oil of S = 0.9 through an orifice meter of size 15 cm diameter fitted in a pipe of 30 cm diameter. The mercury deflection of U tube differential manometer connected on the two sides of the orifice is 50 cm. Assume Cd of orifice meter as 0.64.

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 15

1.269)A submarine moves horizontally in sea and has its axis 15 m below the surface of water. A pitot static tube properly placed just in front of the submarine along its axis and is connected to the two limbs of a U - tube containing mercury. The difference of mercury level is found to be170 mm. Find the speed of submarine knowing that the sp. gr of sea water is 1.026. 1.270)A submarine fitted with a Pitot tube move horizontally in sea. Its axis is 20m below surface of water. The Pitot tube placed in front of the submarine along its axis is connected to a differential mercury manometer showing the deflection of 20cm. Determine the speed of the submarine.[MAY 05] 1.271)A pitot-static probe is used to measure the velocity of an aircraft flying at 3000 m. If the differential pressure reading is 3 kPa, determine the velocity of the aircraft. [MAY 08] 1.272)A 15 cm diameter vertical pipe is connected to 10 cm diameter vertical pipe with a reducing socket. The pipe carries a flow of 1001/s. At point 1 in 15 cm pipe gauge pressure is 250 kPa. At point 2 in the 10 cm pipe located 1.0 m below point 1 the gauge pressure is 175 kPa. Find whether the flow is upwards / downwards and Head loss between the two points. 1.273)Water enters a reducing pipe horizontally and comes out vertically in the downward direction. If the inlet velocity is 5 m/sec and pressure is 80 kPa (gauge) and the diameters at the entrance and exit sections are 300 mm and 200 mm respectively. Calculate the components of the reaction acting on the pipe.

UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS PART - A

2.1)How are fluid flows classified? [JUN 12] 2.2)Write down Hagen Poiseuilles equation for viscous flow through a pipe. 2.3)Write down Hagen Poiseuilles equation for laminar flow.[MAY 05, DEC 12] 2.4)Write the Hagen Poiseuilles Equation and enumerate its importance.[MAY 11] 2.5)State Hagen Poiseuilles formula for flow through circular tubes.[JUN 12] 2.6)Write down the Darcy - Weisbachs equation for friction loss through a pipe [DEC 09, MAY 11] 2.7)What is the relationship between Darcy Friction factor, Fanning Friction Factor and Friction coefficient?[JUN12] 2.8)Mention the types of minor losses.[MAY 10] 2.9)List the minor losses in flow through pipe.[MAY 05, JUN 07] 2.10)What are minor losses? Under what circumstances will they be negligible?[JUN12] 2.11)Distinguish between the major loss and minor losses with reference to flow through pipes. [JUN 09] 2.12)List the causes of minor energy losses in flow through pipes.[DEC09] 2.13)What are the losses experienced by a fluid when it is passing through a pipe? 2.14)What is a minor loss in pipe flows? Under what conditions does a minor loss become a major loss? 2.15)What do you understand by minor energy losses in pipes?[DEC 08] 2.16)List out the various minor losses in a pipeline

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 16

2.17)What are major and minor losses of flow through pipes? [JUN 07, DEC 07, 12, MAY 10] 2.18)List the minor and major losses during the flow of liquid through a pipe. [MAY 08] 2.19)Enlist the various minor losses involved in a pipe flow system.[DEC 08] 2.20)What factors account in energy loss in laminar flow. [JUN 12] 2.21)Differentiate between pipes in series and pipes in parallel.[DEC 06] 2.22)What is Darcy's equation? Identify various terms in the equation.[MAY 11] 2.23)What is the relation between Darcy friction factor, fanning friction factor and friction coefficient?[DEC 10] 2.24)When is the pipe termed to be hydraulically rough?[DEC 09] 2.25)What is the physical significance of Reynold's number?[JUN, DEC 07] 2.26)Define Reynolds Number.[DEC 12] 2.27)Write the Navier's Stoke equations for unsteady 3 - dimensional, viscous, incompressible and irrotational flow. [MAY 08] 2.28)Define Moodys diagram 2.29)What are the uses of Moodys diagram? [DEC08, 2012] 2.30)Write down the formulae for loss of head due to (1). sudden enlargement in pipe diameter (2). Sudden contraction in pipe diameter and (3). Pipe fittings. 2.31)Define (i) relative roughness and (ii) absolute roughness of a pipe inner surface. 2.32)How does surface roughness affect the pressure drop in a pipe if the flow is turbulent? [DEC 13] 2.33)A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in parallel. How would you compare the flow rates and pressure drops in these two pipes?[DEC 13] 2.34)What do you mean by flow through parallel pipes?[JUN 13] 2.35)What is equivalent pipe? 2.36)What is the use of Dupuits equations? 2.37)What is the condition for maximum power transmission through a pipe line? 2.38)Give the expression for power transmission through pipes?[DEC 08] 2.39)Write down the formula for friction factor of pipe having viscous flow. 2.40)Define boundary layer and boundary layer thickness.[DEC 2007, 2012] 2.41)Define boundary layer thickness.[JUN 06, DEC 09] 2.42)What is boundary layer? Give its sketch of a boundary layer region over a flat plate. [MAY 03] 2.43)What is boundary layer? Why is it significant? [DEC 09] 2.44)Define boundary layer and give its significance. [MAY 10] 2.45)What is boundary layer and write its types of thickness?[DEC 2005, 2006] 2.46)What do you understand by the term boundary layer? [DEC 08] 2.47)Define the following (i) laminar boundary layer (ii) turbulent boundary layer

(iii) Laminar sub layer.

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 17

2.48)What is a laminar sub layer? [DEC 10] 2.49)Define momentum thickness and energy thickness. [JUN 2007, 2012] 2.50)Define the term boundary layer.[JUN 09] 2.51)Define the terms boundary layer, boundary thickness. [DEC 08] 2.52)What is boundary layer separation?[DEC 12] 2.53)Define the following:

(i) Displacement thickness ( ii) Momentum thickness (iii) Energythickness. 2.54)What do you mean by displacement thickness and momentum thickness?[DEC08] 2.55)What do you understand by hydraulic diameter? [DEC 11] 2.56)What is hydraulic gradient line? [JUN 09] 2.57)Define hydraulic gradient line and energy gradient line. 2.58)Brief on HGL. [MAY 11] 2.59)Differentiate between Hydraulic gradient line and total energy line. [DEC 03, MAY 05, 2010, JUN2007, 2009] 2.60)What is T.E.L?[DEC 09] 2.61)Distinguish between hydraulic and energy gradients. [DEC 11] 2.62)Differentiate hydraulic gradient line and energy gradient line.[JUN 14] 2.63)What are stream lines, streak lines and path lines in fluid flow?[DEC 2006, 2009] 2.64)What do you mean by Prandtls mixing length? 2.65)Draw the typical boundary layer profile over a flat plate. 2.66)Define flow net.[DEC 08] 2.67)What is flow net and state its use?[MAY 11] 2.68)Define lift. [DEC 05] 2.69)Define the terms: drag and lift.[DEC 2007, JUN 09] 2.70)Define drag and lift co-efficient. 2.71)Give the expression for Drag coefficient and Lift coefficient.[MAY 11] 2.72)Considering laminar flow through a circular pipe, draw the shear stress and velocity distribution across the pipe section. [DEC 10] 2.73)Considering laminar flow through a circular pipe, obtain an expression for the velocity distribution. [DEC 12] 2.74)A circular and a square pipe are of equal sectional area. For the same flow rate, determine which section will lead to a higher value of Reynolds number.[DEC 11] 2.75)A 20cm diameter pipe 30km long transport oil from a tanker to the shore at 0.01m3/s. Find the Reynolds number to classify the flow. Take the viscosity = 0.1 Nm/s2 and density = 900 kg/m3 for oil.[MAY 03] 2.76)Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s.[MAY 10]

PART - B 2.77)What are the various types of fluid flows? Discuss [DEC 10] 2.78)Define minor losses. How they are different from major losses?[JUN 09] 2.79)Discuss on various minor losses in pipe flow. [DEC 13]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 18

hf= 8 fLQ2/g2D5 [DEC 09] 2.102)Derive Eulers equation of motion for flow along a stream line. What are the

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 19

1. Displacement thickness 2. Momentum thickness 3. Energy thickness [JUN 14] 2.120)Find the displacement thickness momentum thickness and energy thickness for the velocity distribution in the boundary layer given by (u/v) = (y/), where u is the velocity at a distance y from the plate and u=U at y=, where = boundary layer

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 20

thickness. Also calculate (*/). [DEC07, MAY 10] 2.121)Explain the concept of boundary layer in pipes for both laminar and turbulent flows with neat sketches.[DEC 13] 2.122)Derive an expression for the velocity distribution for viscous flow through a circular pipe. [JUN 07] 2.123)Write a brief note on velocity potential function and stream function. [JUN09] 2.127) Derive an expression for the velocity distribution for viscous flow through a circular pipe. Also sketch the distribution of velocity cross section of the pipe. [DEC11]

PROBLEMS 2.124)A 20 cm diameter pipe 30 km long transports oil from a tanker to the shore at 0.01m3/s. Find the Reynolds number to classify the flow. Take viscosity and density for oil. 2.125)A pipe line 20cm in diameter, 70m long, conveys oil of specific gravity 0.95 and viscosity 0.23 N.s/m2. If the velocity of oil is 1.38m/s, find the difference in pressure between the two ends of the pipe. [JUN 12] 2.126)Oil of absolute viscosity 1.5 poise and density 848.3kg/m3 flows through a 300mm pipe. If the head loss in 3000 m, the length of pipe is 200m, assuming laminar flow, find (i) The average velocity, (ii) Reynoldss number and (iii) Friction factor.[JUN12] 2.127)An oil of specific gravity 0.7 is flowing through the pipe diameter 30cm at the rate of 500litres/sec. Find the head lost due to friction and power required to maintain the flow for a length of 1000m. Take = 0.29 stokes.[DEC 2008, JUN09] 2.128)A pipe line 10km, long delivers a power of 50kW at its outlet ends. The pressure at inlet is 5000kN/m2 and pressure drop per km of pipeline is 50kN/m2. Find the size of the pipe and efficiency of transmission. Take 4f = 0.02. [DEC 05] 2.129)A lubricating oil flows in a 10 cm diameter pipe at 1 m/s. Determine whether the flow is laminar or turbulent. 2.130)For the lubricating oil 2 = 0.1Ns /m and = 930 kg/m3. Calculate also transition and turbulent velocities.[MAY 11]

2.131)Oil of ,mass density 800kg/m3 and dynamic viscosity 0.02 poise flows through 50mm diameter pipe of length 500m at the rate of 0.19 L/ sec. Determine 1. Reynolds number of flow 2. Center line of velocity 3. Pressure gradient 4. Loss of pressure in 500m length 5. Wall shear stress 6. Power required to maintain the flow. [JUN 12] 2.132)In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the center line) is measured to be 6m/s. Determine the velocity at the center of the pipe.[MAY 08] 2.133)A pipe 85m long conveys a discharge of 25litres per second. If the loss of head is 10.5m. Find the diameter of the pipe take friction factor as 0.0075.[DEC 09] 2.134)A smooth pipe carries 0.30m3/s of water discharge with a head loss of 3m per

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 21

100m length of pipe. If the water temperature is 20C, determine diameter of the pipe. [JUN 12] 2.135)Water is flowing through a pipe of 250 mm diameter and 60 m long at a rate of 0.3 m3/sec. Find the head loss due to friction. Assume kinematic viscosity of water 0.012 stokes. 2.136)Consider turbulent flow (f = 0.184 Re-0.2) of a fluid through a square channel with smooth surfaces. Now the mean velocity of the fluid is doubled. Determine the change in the head loss of the fluid. Assume the flow regime remains unchanged. What will be the head loss for fully turbulent flow in a rough pipe? [DEC 13] 2.137)A pipe of 12cm diameter is carrying an oil ( = 2.2 Pa.s and = 1250 kg/m3) with a velocity of 4.5 m/s. Determine the shear stress at the wall surface of the pipe, head loss if the length of the pipe is 25 m and the power lost.[DEC 11] 2.138)Find the head loss due to friction in a pipe of diameter 30cm and length 50cm, through which water is flowing at a velocity of 3m/s using Darcys formula.[DEC 08] 2.139)For a turbulent flow in a pipe of diameter 300 mm, find the discharge when the center-line velocity is 2.0 m/s and the velocity at a point 100 mm from the center as measured by pitot-tube is 1.6 m/s.[MAY 10] 2.140)A laminar flow is taking place in a pipe of diameter 20cm. The maximum velocity is 1.5m/s. Find the mean velocity and radius at which this occurs. Also calculate the velocity at 4cm from the wall pipe.[JUN09] 2.141)Water is flowing through a rough pipe of diameter 60 cm at the rate of 600litres/second. The wall roughness is 3 mm.Find the power loss for 1 km length of pipe. 2.142)Water flows in a 150 mm diameter pipe and at a sudden enlargement, the loss of head is found to be one-half of the velocity head in 150 mm diameter pipe. Determine the diameter of the enlarged portion. 2.143)A 150mm diameter pipe reduces in diameter abruptly to 100mm diameter. If the pipe carries water at 30 liters per second, calculate the pressure loss across the contraction. The coefficient of contraction as 0.6.[DEC 12] 2.144)A pipe line carrying oil of specific gravity 0.85, changes in diameter from 350mm at position 1 to 550mm diameter to a position 2, which is at 6m at a higher level. If the pressure at position 1 and 2 are taken as 20N/cm2 and 15N/cm2

respectively and discharge through the pipe is 0.2m3/s. Determine the loss of head. [JUN 07]

2.145)A pipe line carrying oil of specific gravity 0.87, changes in diameter from 200mm at position A to 500mm diameter to a position B, which is at 4m at a higher level. If the pressure at position A and B are taken as 9.81N/cm2 and 5.886N/cm2 respectively and discharge through the pipe is 200 litres/s. Determine the loss of head and direction of flow.[DEC 08] 2.146)A 30cm diameter pipe of length 30cm is connected in series to a 20 cm

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 22

diameter pipe of length 20cm to convey discharge. Determine the equivalent length of pipe diameter 25cm, assuming that the friction factor remains the same and the minor losses are negligible.[MAY 03] 2.147)A pipe of 0.6m diameter is 1.5 km long. In order of augment the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. Neglecting minor losses. Find the increase in discharge, if friction factor f= 0.04. The head at inlet is 40m.[DEC 2004, 2005, 2012] 2.148)A pipe of 10 cm in diameter and 1000 m long is used to pump oil of viscosity 8.5 poise and specific gravity 0.92 at the rate of1200 L/min. The first 30 m of the pipe is laid along the ground sloping upwards at 10 to the horizontal and remaining pipe is laid on the ground sloping upwards 15 to the horizontal. State whether the flow is laminar or turbulent? Determine the pressure required to be developed by the pump and the power required for the driving motor if the pump efficiency is 60%. Assume suitable data for friction factor, if required. [DEC 10] 2.149)Oil with a density of 900 kg/m3and kinematic viscosity of 6.210-4m2is being discharged by a 6 mm dia, 40 m long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 3 m. Neglecting the minor losses, determine the flow rate of oil through the pipe.[DEC 11] 2.150)The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe is 500m. Find the loss of head due to friction, if f = 0.008.[DEC 05] 2.151)A 200mm diameter (f = 0.032) 175m long discharges a 65mm diameter water jet into the atmosphere at a point which is 75m below the water surface at intake. The entrance to the pipe is reentrant with ke = 0.92 and the nozzle loss coefficient is 0.06. Find the flow rate and the pressure head at the base of the nozzle. [MAY 11] 2.152)A pipe line 2000m long is used for power transmission 110kW is to be transmitted through a pipe in which water is having a pressure of 5000kN/m2 at inlet is flowing. If the pressure drop over a length of a pipe is 1000kN/m2 and coefficient of friction is 0.0065, find the diameter of the pipe and efficiency of transmission. [JUN12] 2.153)A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of 200 mm. The pressure intensities in the large and small pipe are given as 15 N/cm2 and 10 N/cm2 respectively. Find the loss of head due to contraction, if Cc = 0.62, determine also the rate of flow of water. 2.154)A horizontal pipe line 40 m long is connected to a water tank at one end and discharges freely into the atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is 150 mm diameter and its diameter is suddenly enlarged to 300 mm. The height of water level in the tank is 8 m above the centre of the pipe. Considering all losses of head which occur, determine the rate of flow. Take f = 0.01 for both sections of the pipe. [JUN 13] 2.155)A 15cm diameter vertical pipe is connected to 10cm diameter vertical pipe with a

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 23

reducing socket. The pipe carries a flow of 100 l/s. At a point 1 in 15cm pipe gauge pressure is 250kPa. At point 2 in the 10cm pipe located 1m below point 1 the gauge pressure is 175kPa. Find weather the flow is upwards /downwards & Head loss between the two points[DEC08] 2.156)The rate of flow of water through a horizontal pipe is 0.25 m3/sec. The diameter of the pipe, which is 20 cm, is suddenly enlarged to 40 cm. The pressure intensity in the smaller pipe is 11.7 N/cm2. Determine the loss of head due to sudden enlargement and pressure intensity in the larger pipe, power loss due to enlargement. [JUN 0 9 ] 2.157)A 45 reducing bend is connected to a pipe line. The inlet and outlet diameters of the bend being 600mm and 300mm respectively. Find the force exerted by water on the bend, if the intensity of pressure at inlet to bend is 8.829N/cm2 and the rate of flow of water is 600 liters/s. [DEC 07] 2.158)Horizontal pipe carrying water is gradually tapering. At one section the diameter is 150mm and the flow velocity is 1.5m/s. If the drop pressure is 1.104bar is reduced section, determine the diameter of that section. If the drop is 5kN/m2, what will be the diameter Neglect the losses? [DEC 09] 2.159)The rate of flow of water through a horizontal pipe is 0.3m3/sec. The diameter of the pipe, which is 25cm, is suddenly enlarged to 50 cm. The pressure intensity in the smaller pipe is 14N/cm2. Determine the loss of head due to sudden enlargement, pressure intensity in the larger pipe power lost due to enlargement. [DEC 03] 2.160)Water at 15C ( =999.1 kg/m3and = 1.138 x 10-3kg/m. s) is flowing steadily in a30-m-long and 4 cm diameter horizontal pipe made of stainless steel at a rate of 8 L/s. Determine (i) the pressure drop, (ii) the head loss, and (iii) the pumping power requirement to overcome this pressure drop. Assume friction factor for the pipe as 0.015. [MAY 08] 2.161)The discharge of water through a horizontal pipe is 0.25m3/s. The diameter of above pipe which is 200mm suddenly enlarges to 400mm at a point. If the pressure of water in the smaller diameter of pipe is 120kN/m2, determine loss of head due to sudden enlargement; pressure of water in the larger pipe and the power lost due to sudden enlargement. [JUN 09] 2.162)A pipe of varying sections has a sectional area of 3000, 6000 and 1250 mm2 at point A, B and C situated 16 m, 10 m and 2 m above the datum. If the beginning of the pipe is connected to a tank which is filled with water to a height of 26 m above the datum, find the discharge, velocity and pressure head at A, B and C. Neglect all losses. Take atmospheric pressure as 10 m of water. 2.163)An existing 300mm diameter pipeline of 3200m length connects two reservoirs having 13m difference in their water levels. Calculate the discharge Q1. If a parallel pipe 300mm in diameter is attached to the last 1600m length of the above existing pipe line, find the new discharge Q2. What is the change in discharge? Express it as a % of

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 24

Q1. Assume friction factor f = 0.14 in Darcy Weisbach formula.[JUN 09] 2.164)Two reservoirs with a difference in water surface elevation of 15 m are connected by a pipe line ABCD that consists of three pipes AB, BC and CD joined in series. Pipe AB is 10 cm in diameter, 20 m long and has f = 0.02. Pipe BC is of 16 cm diameter, 25 m long and has f = 0.018. Pipe CD is of 12 cm diameter, 15 m long and has f = 0.02. The junctions with the reservoirs and between the pipes are abrupt. (a) Calculate the discharge (b) What difference in reservoir elevation is necessary to have a discharge of 20 litres/sec? Include all minor losses. 2.165)Two tanks of fluid ( = 998 kg/m3 and = 0.001 kg/ms.) at 20C are connected by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm higher than the surface of tank 2. Estimate the flow rate in m3/h. Is the flow laminar? For what tube diameter will Reynolds number be 500?[DEC 13] 2.166)Three pipes of 400mm, 350mm and 300mm diameter connected in series between two reservoirs. With difference in level of 12m. Friction factor is 0.024, 0.021 and 0.019 respectively. The lengths are 200m, 300m and 250m. Determine flow rate neglecting the minor losses.[DEC 09] 2.167)Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths450 m, 255 m and 315 m respectively are connected in series. The difference in water surface levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of friction are 0.0075, 0.0078and 0.0072 respectively considering: the minor losses and by neglecting minor losses.[DEC 11] 2.168)Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 300 m, 170 m and 210 m respectively are connected in series. The difference in water surface levels in two tanks is 12 m. Determine the rate of flow of water if coefficients of friction are 0.005, 0.0052 and 0.0048 respectively considering: the minor losses and by neglecting minor losses[JUN 2012] 2.169)Three pipes connected in series to make a compound pipe. The diameters and lengths of pipes are respectively, 0.4m, 0.2m, 0.3m and 400m, 200m, 300m. The ends of the compound pipe are connected to 2 reservoirs whose difference in water levels is 16m. The friction factor for all the pipes is same and equal to 0.02. The coefficient of contraction is 0.6. Find the discharge through the compound pipe if, minor losses are negligible. Also find the discharge if minor losses are included. [DEC 10] 2.170)A compound piping system consists of 1800 m of 0.5 m, 1200 m of 0.4 m and 600 m of 0.3 m new cast-iron pipes connected in series. Convert the system to (i) an equivalent length of0.4 m diameter pipe and (ii) an equivalent size of pipe of 3600 m length. [MAY 03] 2.171)A pipe line of 600 mm diameter is 1.5 km long. To increase the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. If f = 0.01 and head at inlet is 30 m, calculate the increase in discharge.

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 25

2.172)A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another line of same diameter is introduced in parallel to the first in second half of the length. Neglecting the minor losses, find the increase in discharge if 4f = 0.04. The head at inlet is 30cm. [MAY 11] 2.173)Two pipes of 15cm and 30cm diameters are laid in parallel to pass a total discharge of 100 litres per second. Each pipe is 250m long. Determine discharge through each pipe. Now these pipes are connected in series to connect two tanks 500m apart, to carry same total discharge. Determine water level difference between the tanks. Neglect the minor losses in both cases, f=0.02 fn both pipes.[JUN07] 2.174)Two pipes of diameter 40 cm and 20 cm are each 300 m long. When the pipes are connected in series and discharge through the pipe line is0.10 m3/sec, find the loss of head incurred. What would be the loss of head in the system to pass the same total discharge when the pipes are connected in parallel? Take f = 0.0075 for each pipe. [JUN 2007, 2012, DEC 10] 2.175)A main pipe divides into two parallel pipes, which again forms one pipe. The length and diameter for the first parallel pipe are 2000m and 1m respectively, while the length and diameter of second parallel pipe are 200m and 0.8m respectively. Find the rate of flow in each parallel pipe, if total flow in the main is 3m3/s. The coefficient of friction for each parallel pipe is same and equal to 0.005.[JUN 07] 2.176)The main pipe is divided into two parallel pipes which again forms one pipe, the first parallel pipe has length of 1000 m and diameter of 0.8 m. The second parallel pipe has length of 1000 m and diameter of 0.6 m. The coefficient friction for each parallel pipe is 0.005. If the total rate of flow in the main pipe is 2 m3 /sec, find the rate of flow in each parallel pipe.[JUN 14] 2.177)For a town water supply, a main pipe line of diameter 0.4 m is required. As pipes more than 0.35m diameter are not readily available, two parallel pipes of same diameter are used for water supply. If the total discharge in the parallel pipes is same as in the single main pipe, find the diameter of parallel pipe. Assume co- efficient of discharge to be the same for all the pipes.[MAY 10] 2.178)Two pipes of identical length and material are connected in parallel. The diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to be the same in both cases and disregarding minor losses, determine the ratio of the flow rates in the two pipes.[MAY 08] 2.179)A pipe line 30cm in diameter and 3.2m long is used to pump up 50Kg per second of oil whose density is 950 Kg/m3 and whose kinematic viscosity is 2.1 strokes, the center of the pipe line at the upper end is 40m above than the lower end. The discharge at the upper end is atmospheric. Find the pressure at the lower end and draw the hydraulic gradient and total energy line. [MAY 11] 2.180)Two water reservoirs A and B are connected to each other through a 50 m long, 2.5 cm C.I pipe with a sharp-edged entrance. The pipe also involves a swing check valve and a fully open gate valve. The water level in both reservoirs is the same, but

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 26

reservoir A is pressurized by compressed air while reservoir B is open to the atmosphere. If the initial flow rate through the pipe is 1.5l/s, determine the absolute air pressure on top of reservoir A Take the water temperature to be 25C. [DEC11] 2.181)When water is being pumped is a pumping plant through a 600mm diameter main, the friction head was observed as 27m. In order to reduce the power consumption, it is proposed to lay another main of appropriate diameter along the side of existing one, so that the two pipes will work in parallel for the entire length and reduce the friction head to 9.6m only. Find the diameter of the new main if with the exception of diameter; it is similar to the existing one in all aspects.[DEC 07] 2.182)Determine the Pressure gradient The shear stress at the two horizontal parallel plates and Discharge per meter width for the laminar flow of oil with maximum velocity 2m/s

between two horizontal parallel fixed plates which are 10cm apart. Given = 2.4525 Ns/m2 [MAY 11]

2.183)In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the centerline) is measured to be 6 m/s. Determine the velocity at the center of the pipe.[MAY 08] 2.184)A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/h. If laminar boundary layer exists up to a value of Rexequal to 3 x 105, find the maximum distance up to which laminar boundary layer exists and find its maximum thickness. Assume kinematic viscosity of air as 1.49 x 10-5m2/s. [MAY 03] 2.185)Air is flowing over a flat plate with a velocity of 5 m/s. The length of the plate is 2.5 m and width 1 m. The kinematic viscosity of air is given as 0.15 x 10-4m2/s.

Find the (i) boundary layer thickness at the end of plate (ii) shear stress at 20 cm from the leading edge (iii) shear stress at 175 cm from the leading edge (iv) Drag force on one side of the plate. (v) Take the velocity profile over a plate as and the density of air1.24

kg/m3. 2.186)A plate of 600mm length and 400mm wide is immersed in a fluid of specific gravity 0.9 and kinematic viscosity of = 10-4 m2/s. The fluid is moving with velocity of 6m/s. Determine

Boundary layer thickness Shear stress at the end of the plate

2.187)Drag force on one side of the plate. [DEC 12] 2.188)Water at 20 C enters a pipe with a uniform velocity (U) of 3m/s. What is the distance at which the transition (x) occurs from a laminar to a turbulent boundary

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 27

layer? If the thickness of this initial laminar boundary layer is given by 4.91(vx/U) what is its thickness at the point of transition?(v kinematic viscosity).[MAY 11] 2.189)A flat plate 1.5 m x 1.5 m moves at 50 km/h in stationary air of density 1.15 kg/m3. If the co-efficient of drag and lift are 0.15 and 0.75 respectively, determine The Lift force, Drag force, the resultant force and the power required to set the plate in motion. [DEC 07]

2.190)A jet plane which weighs 29430 N and has the wing area of 20m2 flies at the velocity of 250km/hr. When the engine delivers 7357.5kW. 65% of power is used to overcome the drag resistance of the wing. Calculate the coefficient of lift and coefficient of drag for the wing. Take density of air = 1.21 kg/m3[JUN09] 2.191)For the velocity profile in laminar boundary layer as u/U = 3/2 (y/)-1/2(y/) 3. Find the thickness of the boundary layer and shear stress, 1.8m from the leading edge of a plate. The plate is 2.5 m long and 1.5 m wide is placed in water, which is moving with a velocity of 15 cm/sec. Find the drag on one side of the plate if the viscosity of water is 0.01 poise.[DEC 03] 2.192)Consider flow of oil through a pipe of 0.3m diameter. The velocity distribution is parabolic with maximum velocity of 3 m/s at the pipe centre. Estimate the shear stress at the pipe wall and within the fluid 50mm from the pipe wall. The viscosity of the oil is 1.7Pa.s.[DEC 12] 2.193)The velocity distribution for flow over a plate is given by u = 2y y2 where u is the velocity in m/sec at a distance y meters above the plate. Determine the velocity gradient and shear stress at the boundary and 0.15m from it. Dynamic viscosity of the fluid is 0.9Ns/m2 [MAY 10] 2.194)The velocity distribution in the boundary layer is given by u/U = y/, where u is the velocity at the distance y from the plate u = U at y = , being boundary layer thickness. Find the displacement thickness, momentum thickness and energy thickness. [MAY 10] 2.195)The flow rate in a 260mm diameter pipe is 220 litres/sec. The flow is turbulent, and the centerline velocity is 4.85m/s. Plot the velocity profile, and determine the head loss per meter of pipe.[MAY 11]

2.196)The velocity distribution over a plate is given by u = (3/4) * y y2 where u is velocity in m/s and at depth y in m above the plate. Determine the shear stress at a distance of 0.3m from the top of plate. Assume dynamic viscosity of the fluid is taken as 0.95 Ns/m2[MAY 05]

2.197)The velocity distribution over a plate is given by a relation, where y is the vertical distance above the plate in meters. Assuming a viscosity of 0.9Pa.s, find the shear stress at y = 0 and y = 0.15m.[DEC 12] 2.198)An oil of viscosity 0.9Pa.s and density 900kg/m3 flows through a pipe of

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 28

100mm diameter. The rate of pressure drop for every meter length of pipe is 25kPa. Find the oil flow arte, drag force per meter length, pumping power required to maintain the flow over a distance of 1km, velocity and shear stress at 15, from the pipe wall. [DEC 10] 2.199)Consider the flow of a fluid with viscosity m through a circular pipe. The velocity profile in the pipe is given as where is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; is the flow velocity at any position r; and R is the Reynold's number. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe. [MAY 08]

2.200)Velocity components in flow are given by U = 4x, V = -4y. Determine the stream and potential functions. Plot these functions for 60, 120, 180, and 240 and 0, 60, 120, 180, +60, +120, +180. Check for continuity. [DEC 09] 2.201)A fluid of specific gravity 0.9 flows along a surface with a velocity profile given by v = 4y - 8y3m/s, where y is in m. What is the velocity gradient at the boundary? If the kinematic viscosity is 0.36S, what is the shear stress at the boundary? [A.U. DEC 08] 2.202)In a two dimensional incompressible flow the fluid velocities are given by u = x ay and v = - y 4x. Show that the velocity potential exists and determine its form. Find also the stream function.[JUN09] 2.203)A smooth flat plate with a sharp leading edge is placed along a free stream of water flowing at 3m/s. Calculate the distance from the leading edge and the boundary thickness where the transition from laminar to turbulent- flow MAY commence. Assume the density of water as 1000 kg/m3 and viscosity as 1centipoise. [MAY 11] 2.204)A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/hr. If laminar boundary layer exists up to a value of RN = 3 x105, find the maximum distance up to which laminar boundary layer persists and find its maximum thickness. Assume kinematic viscosity of air as 1.49x10-5 m2/s.[DEC 08] 2.205)A power transmission pipe 10 cm diameter and 500 m long is fitted with a nozzle at the exit, the inlet is from a river with water level 60 m above the discharge nozzle. Assume f = 0.02, calculate the maximum power which can be transmitted and the diameter of nozzle required. [DEC 08]

\ 4

UNIT - III - DIMENSIONAL ANALYSIS

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 29

PART - A 3.1)What do you understand by fundamental units and derived units?[MAY 10] 3.2)Differentiate between fundamental units and derived units. Give examples.[DEC 11] 3.3)Define dimensional analysis. 3.4)What do you mean by dimensional analysis?[DEC 09] 3.5)Define dimensional homogeneity. 3.6)What is dimensional homogeneity and write any one sample equation?[DEC 06] 3.7)Explain the term dimensional homogeneity.[DEC 11] 3.8)Give the methods of dimensional analysis. 3.9)State a few applications, usefulness of dimensional analysis.[JUN 07] 3.10)What is a dimensionally homogenous equation? Give example.[DEC 03] 3.11)Cite examplesfordimensionallyhomogeneousandnon-homogeneous equations. [DEC 10] 3.12)Check whether the following equation is dimensionally homogeneous. Q =Cd .a (2 gh). [MAY 11] 3.13)Define Rayleigh's method. 3.14)Give the Rayleigh method to determine dimensionless groups.[DEC 11] 3.15)State any two choices of selecting repeating variables in Buckingham theorem. [MAY 11] 3.16)State Buckinghams theorem.[DEC 2008, 2012] 3.17)What is Buckingham's theorem? 3.18)The excess pressure p inside a bubble is known to be a function of the surface tension and the radius. By dimensional reasoning determine how the excess pressure. Will vary if we double the surface tension and the radius.[DEC 13] 3.19)Distinguish between Rayleigh's method and Buckingham's - theorem.[MAY 11] 3.20)Under what circumstances, will Buckinghams theorem yield incorrect number of dimensionless group? 3.21)State a few applications / usefulness of dimensional analysis. 3.22)Define Euler's number. [JUN 09] 3.23)List out any four rules to select repeating variable. 3.24)Define similitude. 3.25)Give the three types of similarities. 3.26)What are the types of similarities?[DEC 12] 3.27)Define geometric similarity. 3.28)Define kinematic similarity. 3.29)Define dynamic similarity. 3.30)What is meant by dynamic similarity? [DEC08] 3.31)What is dynamic similarity?[DEC 09] 3.32)What is similarity in model study? [MAY 05] 3.33)What is scale effect in physical model study?[DEC 2005, 2006, JUN 2012] 3.34)If two systems (model and prototype) are dynamically similar, is it implied that they are also kinematically and geometrically similar? [JUN12]

• CE6451 FLUID MECHANICS AND MACHINERY QUESTION BANK 30

3.35)Distinguish between a control and differential control volume.[MAY 11] 3.36)Mention the circumstances which necessitate the use of distorted models.[DEC 10] 3.37)Give the types of forces in a moving fluid. 3.38)Give the dimensions of power and specific weight.[DEC 09] 3.39)Define inertia force. 3.40)Define viscous force. 3.41)Define gravity and pressure force. 3.42)Define surface tension force. 3.43)Define dimensionless numbers. 3.44)Give the types