fluid mechanics question bank

ADHIPARASAKTHI ENGINEERING COLLEGE

DEPARTMENT OF CHEMICAL ENGINEERING

CH2203  -  FLUID MECHANICS

QUESTION BANK  SEMESTER III (2012-2013)

UNIT-I INTRODUCTION

PART-A QUESTIONS

1. Define Fluid mechanics.
2. Define the terms fluid and flow.
3. Differentiate ideal and real fluids.
4. Define the Continuum concept of a fluid.
5. Differentiate Compressible and Incompressible fluid.
6. Define Viscosity and give its units.
7. Explain Power law for fluids.
8. What do you mean by Steady and Unsteady flow?
9. Define fluid statics.
10. Define fluid dynamics.
11. Define fluid kinematics.
12. Define Shear stress of fluid.
13. Define Bulk modulus.
14. Define Kinematic viscosity and give its unit.
15. Define Surface tension and give its unit.
16. State the Pascal’s law for pressure at a point.
17. Distinguish between Rotational and Irrotational flow.
18. What do you mean by Uniform and Non-uniform flow?
19. State Newton’s law of viscosity.
20. Differentiate Newtonian and Non-Newtonian fluids.
21. What are time-dependent and time-independent fluids?
22. Draw the Rheological behavior of the fluids.
23. What is the effect of pressure and temperature on viscosity of fluids?
24. Define Reynolds number. Explain its physical significance.
25. State the steady flow energy equation

PART-B QUESTIONS

1. (i) Derive an expression for resultant force on a curve surface due to hydrostatic pressure.

            (ii) Derive the Barometric equation on hydrostatic equilibrium.

2. Explain the rheological behaviour of the following Non-Newtonian fluids;

            (i) Bingham plastic fluids

            (ii) Pseudo-plastic fluids

            (iii) Dilatant fluids

            (iv)Visco-elastic fluids

3. (i) Derive a general equation for variation of pressure due to gravity at various heights in a static fluid.

            (ii) With a neat diagram, explain the principle, working of a differential manometer.

4. (i) Explain with a neat sketch the working of a continuous gravity decanter and derive an expression to estimate the separation time.

        (ii) A continuous gravity decanter is to separate nitrobenzene with a density of 1109 kg/m³ from an aqueous wash liquid having a density of 1020 kg/m³. If the total depth in the separator is 1m and the interface is to be 0.6m from the vessel floor, (a) What should be the height of heavy liquid overflow leg be? (b)How much would an error of 50mm in this height affect the position of the interface?

5. (i) Explain in detail about different types of manometers used for measurement of pressure drop.

            (ii) A manometer inclined at an angle of 30^o to the ground is used to measure the pressure drop across      an airflow line. If the liquid level in the inclined limb is 3.2cm above the liquid level in the vertical limb, estimate the pressure drop in the line. Water is used as the manometric fluid. Density of air and water are 1.2x10^-3 and 1 g/cc.

6. (i) Explain the variation of pressure due to centrifugal field.

            (ii) A tubular centrifuge is to separate chloro-benzene with a density of 1090 kg/m³ from an aqueous wash liquor having a density of 1010 kg/m³. The centrifuge has an inside diameter of 200mm and rotates at 10000rpm. The free liquid surface inside the bowl is 60mm from the axis of rotation. If the centrifuge bowl is to equal masses of two liquids, what should be the radial distance fro the axis to the top of the overflow of the heavy liquid?

7. (i) A 5 mm diameter capillary tube is used as a viscometer for oils. When the flow rate is  0.071 m³/hr, the measured pressure drop per unit length is 375 kPa/m. Estimate the viscosity of the fluid. Is the flow laminar? Can you also estimate the density of the fluid?

(ii) Explain the relationship between friction factor and Reynolds number and relative roughness of the pipe for flow through straight pipe.

8. Derive an expression for finding volumetric flow rate when an incompressible fluid flows through a pipe under laminar conditions. State the assumptions made and the applications of the expression.

9. (i) A small capillary with an inside diameter of 2.222mm and a length of 0.1585m is being used to   continuously measure the flow rate of a liquid having density of 912 kg/m³. The pressure drop reading across the capillary during the flow is 131mm of water (density 996 kg/m³). The measured flow rate is 5.33 x 10^-7 m³/sec of liquid. Neglecting the end effects, calculate the viscosity of the liquid.

         (ii) Whole milk at 293K having a density of 1030 kg/m³ and viscosity of 1.12 cP is flowing at the   rate of 0.605 kg/s in a glass pipe having a diameter of 63.5mm. (a) Calculate the Reynold’s number. Is this turbulent flow? (b) Calculate the flow rate needed in kg/s for a Reynold’s number of 2100 and the velocity in m/s.

10.  (i) What is a balance equation? Illustrate it with an example.

(ii) A viscous liquid at 27°C is flowing through a horizontal tube of 0.3 m long and 1 inch inside diameter. For a pressure drop of 2.75 atm., the flow rate is 11 x 10^-5 m³/min. The density of the fluid may be assumed as 1260 kg/m³. Calculate the viscosity of the fluid.

UNIT-II PRESSURE DISTRIBUTION IN A FLUID

PART-A QUESTIONS

1. Explain Velocity field.
2. Explain Capillarity.
3. State the law of Buoyancy.
4. Define ‘centre of pressure’.
5. Distinguish between Laminar and Turbulent flow.
6. Give the relationship between the head loss and the velocity in laminar and turbulent flow regions.
7. What is meant by Hydrostatic equilibrium?
8. What is meant by stable and unstable equilibrium?
9. Write the ‘Barometric equation’ of fluid static.
10. Distinguish between ‘absolute pressure’ and ‘gauge pressure’.
11. Explain intensity and scale of turbulence.
12. What do you mean by Reynold’s stresses?
13. What is BWG? Give its range.
14. Define ‘Equivalent pipe’.
15. Define Streamline and Stream tube.
16. What is meant by fully developed flow?
17. Define ‘Water hammer’ in pipes.
18. Define Velocity defect.
19. Define the stream function.
20. Bathscaphes are capable of submerging to great depths in the ocean. What is the pressure at a depth of 5 km, assuming that seawater has a constant specific weight of 10.1 kN/m³³.
21. Define manometric pressure.
22. What the different types of manometers?
23. What is meant by Metacentre of a floating body?
24. What is a micro manometer?
25. Why is there a negative sign in the pressure-height relation?

PART-B QUESTIONS

       1. (i) Show that the velocity distribution with respect to radius under laminar flow for a Newtonian fluid  is a parabola and prove that average velocity is half of the maximum velocity for the same.

            (ii) A fire truck is sucking water from a river and delivering through a long hose to nozzle, from which water issues out at 30.48 m/s. The total flow is 2000 lit/min. The hose has a diameter equivalent of 4 inch pipe. The total length of the hose, connected for valves, fittings, entrance, etc., is       91.44m. What power is required for the fire truck’s pump?

       2. (i)Derive the Fanning’s equation using the shear stress distribution in a smooth tube for flow of  incompressible fluids.

            (ii) Glycerin of viscosity 0.9 N-s/m² and density 1260 kg/m³ is pumped along a horizontal pipe 6.5cm       long and 0.01m diameter at a flow rate of 1.8 lit/min. Determine the flow Reynold’s number and         verify whether the flow is laminar or turbulent. Calculate the pressure loss in the pipe due to frictional    effects and calculate the maximum rate of flow for laminar flow condition to prevail.

      3. (i) Glycerine of density 1260 kg/m³ and viscosity of 0.9 N-sec/m² flows inside a horizontal pipe of   6.5m long and 1cm diameter at a flow rate of 1.8 lit/min. Calculate the pressure loss in the pipe.

(ii) The velocity at the centre line when a fluid flows in a tube of 0.1m diameter is 3 m/sec. If the fluid flowing has a density of 1260 kg/m³ and viscosity of 0.9 N-sec/m², determine whether the flow is laminar or turbulent and calculate the pressure gradient.

     

      4. Derive the Hagen-Poiseuille equation for the case of friction loss in laminar flow of incompressible- fluid through a circular tube.

5. Determine the friction factor and the pressure drop for fully developed laminar flow of ethylene glycol  at 40^oC through a 5cm diameter, 50m long tube at a mass flow rate of 0.1 kg/sec. The viscosity and density of ethylene glycol at 40^oC are 0.96x10^-2 kg/m-sec and 1101 kg/m³.

      6. A 20 wt% sucrose solution having a density of 1074 kg/m³ is flowing through the piping system shown below. The flow rate entering the pipe-1 is 1.892 m³/hr. The flow divides equally in each of pipes-3. Calculate (a) the velocity in pipes 2 and 3 (b) the mass velocity in pipes 2 and 3.

7. Oil of specific gravity 0.8 and viscosity 0.8 cP flows through a pipeline which changes in size from 150mm diameter (section A) to 300mm diameter (section B), section B being 4.5m higher than section A. If the gauge pressures at A and B are 200 and 140 kN/m², determine the direction of flow and energy loss when the pipe carries a discharge of  0.11 m³/sec.

      8. Exhaust gases from a power plant passes through a 0.381m x 0.508m rectangular duct at an average velocity of 15.24 m/s. The total length of the duct is 76.2m and there are two 90^o bends (K_f = 0.9). The gas is at room temperature and about 1 atm. The properties are similar to those of air (assume viscosity of air as 0.1 cP). Calculate the pressure drop in the duct and the power required to overcome the pressure losses.

9.  A fluid of constant density is flowing in a laminar flow at steady state in the horizontal ‘x’ direction between two flat and parallel plates. The distance between the two plates in the vertical direction is ‘2y_o’. Using a shell momentum balance, derive the equation for the velocity profile within this fluid and the maximum velocity for a distance L, M in the ‘x’ direction.

10. For a layer of liquid flowing in laminar flow in the ‘z’ direction down a vertical plate, show that the velocity profile is          V_z = [(P g d²)/(2 m)] [1 – (x/d)²]. Where ‘d’ is the thickness of the layer, ‘x’ is the direction from the free surface of the liquid toward the plate and ‘V_z’ is the velocity at a distance ‘x’ from the surface.

11. State and derive Bernoulli’s equation. Discuss on the correction factors to account for frictional losses and pump work. Give the applications of the same.

UNIT-III DIMENSIONAL ANALYSIS AND SIMILITUDE

PART-A QUESTIONS

1. What are the forces acting on a body immersed in a fluid?
2. Define Drag and Drag coefficient.
3. What are Wall drag and Form drag?
4. Define Sphericity.
5. Define Porosity.
6. What are the forces acting on a particle moving through a fluid?
7. Define terminal velocity.
8. Distinguish between Free settling and Hindered settling.
9. Explain the phenomena of Fluidization.
10. What is minimum fluidization velocity?
11. Distinguish between Particulate and Aggregative fluidization.
12. Give the applications of fluidization.
13. What are the advantages and disadvantages of fluidization?
14. What is Dimensional analysis? List the methods also.
15. In making dimensional analysis what rules do you follow for choosing the scaling variables?
16. Define Dimensional homogeneity.
17. What do you mean by a Model and Prototype?
18. Define Froude number. Give its application.
19. State the Buckingham’s p - theorem.
20. Define Euler number. Give its physical significance.
21. Explain Rayleigh’s method of dimensional analysis.
22. Define Weber number. Give its application.
23. What are model or similarity laws? List them.
24. Define Geometric, Kinematic and Dynamic similarity.
25. What do you mean by ‘Scale-up’?

PART-B QUESTIONS

1.  Discuss briefly about the ‘Dimensional analysis’ and its application with an example.

       2. Liquid flows under steady state conditions along an open channel of fixed inclination to the horizontal. On what factors will the depth of the liquid in the channel depend? Obtain a relationship between those factors using dimensional analysis.

       3. Using dimensional analysis, derive an expression for the force exerted on a body immersed in a flowing fluid.

      4. (i) Write a brief note on the similitude and explain the types of similarity.

(ii) Show that Reynolds number is the ratio of inertial force to viscous force from the principles of dynamic similarity.

5. It is found as a result of experiment that the pressure drop between two ends of a pipe, in which a fluid is flowing, is a function the following variables; pipe diameter (D), pipe length (L), fluid velocity (V), fluid density (r), and fluid viscosity (m). Show by dimensional analysis, how these variables are related.

6. Using dimensional analysis, derive an expression for the terminal settling velocity of a solid, which is moving in a static fluid.

7. Derive the equation of continuity (for steady state flow) with neat sketch of mass balance for a pure fluid through a fixed volume (Dx Dy Dz) in space. Give its physical significance and industrial importance.

8. Derive the Reynold’s Transport Theorem and give its applications.

9. Derive the integral linear Momentum equation from the fundamentals.

10. A fluid situation depends on velocity, density, viscosity, surface tension, pressure drop, due to bulk modulus of elasticity and several linear dimensions L1, L2, and L3. Apply dimensional analysis to these variables to find a set of π parameters.

UNIT-IV VISCOUS FLOW IN DUCTS AND BOUNDARY

LAYER FLOW

PART-A QUESTIONS

1. What is Hagen-Poiseuille law? Give its importance.
2. Define fanning friction factor. Give its equation for laminar and turbulent flow.
3. Write the Darcy-Weisbach and Chezy’s equation for energy losses due to friction.
4. Draw the Moody’s friction factor graph for laminar and turbulent flow.
5. Define equivalent diameter for noncircular channels.
6. What are Skin and Form frictions?
7. Write the momentum balance equation for steady state flow of fluid.
8. State the assumptions made in the derivation of the Bernoulli’s equation.
9. Write the Bernoulli’s equation of fluid flow.
10. State Navier–Stoke’s equation.
11. Write Euler’s equation of motion.
12. Define Momentum correction factor.
13. Define kinetic energy correction factor.
14. What are Energy gradient line and Hydraulic gradient line?
15. Define Mass velocity and discuss the advantages of using it.
16. Define Mach number. Give its physical significance.
17. Write the equation of continuity for compressible fluids.
18. What are Asterisk conditions?
19. What are the processes may occur when a compressible fluid flow in a pipe?
20. Write a note on ‘Normal shock waves’.
21. Distinguish between major and minor losses of flow through pipes.
22. Define Boundary layer.
23. Define Boundary layer thickness.
24. Define the term boundary layer separation.
25. Define energy thickness as applicable for a boundary layer.

PART-B QUESTIONS

1. Derive the equation of work for isothermal expansion of compressible fluids.

2. Derive the equation of critical pressure ratio for isentropic flow of compressible fluid through nozzles.

3. (i) Discuss on drag coefficients for different types of particles.

            (ii) A water softener consists of a vertical tube of 50mm diameter and packed to a height of 0.5m             with ion exchange resin particles. The particles may be considered spherical with a diameter of 1.25mm. Water flows over the bed because of gravity as well as pressure difference at the rate of  300cc/sec. If the bed has a porosity of 0.3, calculate the pressure gradient.

4. (i) Discuss the applications of fluidization and give its merits.

            (ii) A bed containing 35000 kg of sand particles (D_P = 0.16mm) is to be fluidized with air at 400^oC          and 20 kg_f/cm² pressure in a cylindrical vessel of 3m in diameter. The density of sand particles is 2.7g/cc. The viscosity of air at operating condition is 0.032 cP. Calculate (a) the minimum height of the fluidized bed, (b) the pressure drop in the fluidized bed, and (c) the critical superficial velocity assuming, e_M = 0.55

5. Explain the types of fluidization and derive an expression for predicting the minimum fluidization velocity from the fundamentals.

6. (i) Explain the mechanism of Fluidization.

            (ii) A water softener consists of a vertical tube of 45mm diameter and packed to a height of 0.45m             with ion-exchange resin particles. The particles may be considered spherical with a diameter of 1.125mm. Water flows over the bed, because of gravity as well as pressure difference, at a rate of 270 ml/sec. The bed has a porosity of 0.3. Calculate the pressure gradient.

7. (i) Explain the concept of ‘Terminal settling velocity’ and derive an equation for the same.

(ii) Particles of sphalerite (sp. gr. = 4) are settling under the force of gravity in CCl₄ at 20⁰C             (sp. gr. = 1.594). The diameter of particles is 0.10mm. What is the settling velocity of the   particles?

8. Crude oil having specific gravity of 0.8 and viscosity of 4 cP is draining by gravity from the bottom of the tank. The depth of liquid above the draw off connection in the tank is 6m. The pipe i.d. is 0.102m. Its length is 45m and contains 90^oelbow (K_f = 0.9) and two gate valves (K_f = 5). The oil discharges into atmosphere 9m below the draw off connection. Estimate the flow rate in m³/hr.

9. (i) Discuss on losses in sudden contraction in pipes and hoe they can be minimized?

(ii)  Water at room temperature is pumped from a reservoir at the top of a mountain through a 15 cm pipe at a velocity of 3.5 m/s. The pipe discharges into the atmosphere at a level of 1000 m above the level in the reservoir. The pipe itself is 1500 m long. If the overall efficiency of the pump is 65%, calculate the power required.

   

10. (i) A fireman with an 8 cm diameter hose directs a jet of water at 60° to the horizontal so as to reach a fire 10 m above the ground level. If the nozzle and the hose diameter are the same and the length of the hose is 30 m, what should be the head developed by the pump? Assume the equivalent roughness of the hose to be ε = 0.0008 m.

(ii) Describe the flow patterns and regions within the turbulent boundary layer.

UNIT-V FLOW MEASUREMENT AND TUBRO MACHINERY

PART-A QUESTIONS

1. List the types of Valves commonly used.
2. What is a steam trap?
3. Define a Pump.
4. Classify the Pumps.
5. What are the types of pumps used in chemical industry?
6. What is the difference between a pump and a turbine?
7. Explain Head developed by a pump. 
8. Explain Cavitation in a pump.
9. Distinguish between static head and a manometric head of a pump.
10. Define NPSH.
11. Draw the performance characteristic curves of centrifugal pump.
12. What type of pump would you select for;

            (i) Transportation of slurries                                ------------    

            (ii) Transportation of viscous liquids.                 ------------    

            (iii) Transportation of toxic or corrosive liquids ------------    

13. Mention the disadvantages of Pitot tube.
14. Distinguish between Fan, blower, and compressor.
15. What are Variable head and Variable area meters?
16. Write short notes on ‘Insertion meters’.
17. Explain ‘Vena contracta’.
18. Distinguish between Venturi and Orifice meters.
19. What are Notch’s and Weir’s?
20. What do you mean by ‘Velocity of approach’ in weirs?
21. What advantages and disadvantages does the orifice have over the venturimeter?
22. The coefficients of the venturimeter and orifice meter depend on which two variables?
23. Mention few instruments for measuring velocity of a flowing fluid.
24. What is a Diffuser type centrifugal pump?
25. What are the various losses occurring in a centrifugal pump?

PART-B QUESTIONS

1.      (i) With a neat sketch, explain the working principle of a Venturi meter and compare it with an Orifice meter.

(ii) A horizontal Venturi meter having a throat diameter of 20mm is set in a 75mm pipe through which water flows at 25^oC. What is the flow rate of water when the mercury manometer reads 500mm? If 10% of the pressure difference is permanently lost, find the power consumption on account of the meter.

      2.  (i) Describe the construction and working of an Orifice meter with a neat diagram.

            (ii) A horizontal Venturi meter having a throat diameter of 20mm is set in a 75mm i.d pipeline. Water       at 30^oC is through the pipe. A mercury manometer measures the pressure difference across the meter. If the manometer reads 40cm, what is the flow rate?

      3. Classify the fluid moving machinery. Discuss the merits, demerits, and limitations in applications of    various types of pumps.

4. With a neat diagram, discuss in detail about the theory and working principle of a centrifugal pump. Explain the characteristic curves of the same.

5. A sharp edged circular orifice is to be used to measure the flow rate of water at 20^oC (r = 1000 kg/m³, m = 1 mPa-sec) in a pipeline with an internal diameter of 250mm. The orifice diameter is 50mm. The reading of a mercury (r = 13600 kg/m³) manometer at the throat position is 242mm. Calculate the flow rate in lit/sec.

6. Describe the construction, working principles, range of operation, and limitations of various types of variable head and variable area meters.

7. Explain in detail about the various machines (fans, blowers, and compressors) that used to transport compressible fluids.

8. A centrifugal pump takes brine from the bottom of a supply tank and delivers it into the bottom of the other tank. The brine level in the discharge tank is 50m above that in the supply tank. The tanks are connected by 200m of 18cm pipe. The flow rate is 50 lit/sec. The line between the tanks has two gate valves, four standard tees, and four elbows. What is the energy cost for running this pump for a 24hr-day?         Data: r = 1180 kg/m³, µ = 1.2 mPa-s, f = 0.004, overall efficiency of pump and motor is 60%, and the energy cost is Rs. 0.80 / kW-hr.

       9. A centrifugal pump takes brine from a supply tank and delivers it into the open top of the experimental tower. The liquid level in the experimental tower is 50m above that in the supply tank. The tanks are connected by 200m of 18cm pipe. The flow rate is 50 lit/sec. Calculate the power required by the pump, if the overall efficiency is 60% Data: r = 1180 kg/m³, µ = 1.2 mPa-s.

     10. A pump draws a solution of specific gravity 1.84 from a storage tank through a 75mm pipe. The efficiency of the pump is 65%. The velocity in the suction line is 0.9m/s. The pump discharges through a 500mm pipe to an overhead tank. The end of the discharge pipe is 15m above the level of the solution in the feed tank. Friction losses in the entire piping system are 29.9 J/kg. (a) What pressure must the pump develop? (b) What is the power of the pump?