4HE Fluid Mechanics - October 1999

Part A (20 x 2 = 40 marks)

- Define the term 'Static head'.
- State Bernoulli equation. Write dimensions for each term involved.
- Differentiate between absolute viscosity and kinematic viscosity. Write the units.
- The coefficient of discharge for a given orifice is a function of ___________and ___________.
- Define 'Equivalent diameter' for fluid flow through ducts of noncircular diameter.
- Write the physical significance of Mach number.
- What is meant by 'skin friction'?
- Explain the terms maximum velocity and average velocity for a flow of fluid in a circular pipe.
- Write Blake-Plummer equation for packed beds.
- State Darcy's law.
- The velocity gradient, beyond the boundary layer is equal to _________.
- Name two types of fluidization and give two important industrial application.
- How will you calculate the head developed by a pump?
- Write any four important advantages of multistage compressors.
- Pump size is determined on the basis of __________and_____________.
- Determine the density of air under a vacuum of 445 mm Hg at 45
^{o}C. - Write the working principles of ultrasonic flow meters.
- What is meant by loading in a packed tower?
- Write a short note on positive displacement pumps.
- Write momentum equation for compressible flow.
- (a) Develop a differential form of expression for the estimation of pressure filed within a static fluid. (6)
- (a) Calculate the hydraulic mean diameter of the annular space between a 4 cm and 6 cm tubes. (4)
- (a) Using Bernoulli's equation, derive an equation for the estimation of flow rate through venturimeter. (6)
- (a) For a circular pipe of circular cross section, from the first principles prove that
- (a) Water flows through an orifice of 15 mm diameter in a 75 mm pipe at a rate of 600 cc/sec. What is the difference in level on a water manometer connected across the orifice? The discharge coefficient may be taken as 0.62 and the viscosity of water is 1 cP, and density is 1 g/cc. (8)
- (a) A rotameter has a tube of 0.3 m long, which has an internal diameter of 25 mm at the top and 20 mm at the bottom. The diameter of the float is 20 mm and the specific gravity is 4.8 and its volume is 6.6 cc. If the coefficient of discharge is 0.72, at what height will the float be when metering water at 100 cc/sec. (8)
- (a) Briefly discuss the following: (4)
- Particulate fluidization
- Aggregative fluidization
- (a) Using Ergun's equation determine the minimum velocity of water to start fluidization of spherical particles of diameter 1 mm packed in a tube of 10 mm diameter. Porosity = 0.45
- (a) Write briefly the characteristic features and industrial applications of blowers and compressors. (4)
- Manometric head
- Manometric effficiency
- (a) A centrifugal pump is to be used to extract water from a condenser in which the vacuum is 640 mm of Hg. At the rated discharge the net positive suction head must be at least 3 meter above the cavitation vapor pressure of 710 mm Hg. If losses in a suction pipe account for a head of 1.5 m, what must be the least height of liquid level in the condenser above the pump inlet. (8)
(b) With a neat sketch, briefly discuss the working principles of a diaphragm pump. Give any two important applications. (4).

Part B (5 x 12 = 60 marks)

(b) Derive an expression for the estimation of pressure drop in a centrifuge. (4)

(c ) State Newton's law. Give any four examples of non-Newtonian fluids. (2)

Or

(b) A stream of droplets of liquid formed rapidly at an orifice submerged in a second immiscible fluid. It was found that the mean size of the droplets was influenced by the orifice diameter, velocity of liquid, interfacial tension, viscosity of the dispersed phase, density of both dispersed and continuous phases and the acceleration due to gravity. Using dimensional analysis approach obtain a relation between the mean diameter and the other variables. (6)

(c ) Define the term 'roughness factor' (2)

(b) Find the drop in pressure due to the friction in a pipe of 250 m long and 125 mm diameter, when water is flowing at a rate of 0.05 m^{3}/sec. The pipe is of glazed porcelain Absolute roughness k = 0.0015 mm; (R/r v^{2} ) = 0.0017 (6)

Or

U_{x}/U_{max} = 1 - 4S^{2}/d^{2}

Where S is the distance from the axis of the pipe and d is the diameter of the pipe. (6)

(b) Derive Hagen-Poiseuille's equation. Explain the significance of the equation. (6)

(b) Write a note on weirs and give four industrial applications. (4)

Or

(b) What is meant by Doppler's effect? How is it used in the flow measurements? (4)

(b) From the first principles derive Ergun's equation, for the determination of pressure drop in a packed tower and briefly discuss the application. (8)

Or

Viscosity of water = 1 cP

Density of particles = 1500 kg/m

Assuming an wall factor of 1.067 and necessary assumptions and mention clearly. (8)

(b) Define terminal settling velocity. Discuss briefly about three ranges of operation. (4)

(b) (i) Discuss briefly about centrifugal pumps. (4)

(ii) How will you define the following performance measurements for the case of centrifugal pumps? (4)

Or