- With a neat sketch, compare the velocity profiles for laminar and turbulent flow of a fluid in a pipeline.
- Indicate the methods to reduce
(i) skin frictional losses

(ii) form frictional losses. - Calculate the hydraulic radius for flow of fluid through a rectangular duct of size 0.5 m x 0.3 m.
- With a neat diagram, illustrate the relation between friction factor and Reynolds number, for laminar and turbulent flows in circular ducts, indicating the effect of roughness.
- The relation between frictional pressure drop (Dp) and volumetric flow rate (Q) for
flow through pipelines is given by
What is the value of 'n' forDp = cQ ^{n}; where c is a constant.(i) laminar flow

(ii) turbulent flow through very smooth pipe

(iii) turbulent flow through very rough pipe - Draw the shape of nozzles, that is needed for accelerating the flow velocity, for the following flow conditions, indicating the flow direction:
(i) subsonic flow to soinc flow

(ii) sonic to supersonic flow

(iii) subsonic to supersonic flow - Draw a neat sketch showing the development of boundary layer for laminar flow in pipe, also indicate the shape of the velocity profiles at developing and developed sections.
- How does the pressure drop vary with the flow rate in a rota-meter, and in orifice meter?
- The pressure drop between upstream and throat of venturi meter is 100 cm of the flowing fluid. What is the pressure drop if the volumetric flow rate is doubled?
- Compare the manometer readings of orifice meter and venturi meter for a flowrate of Q through a pipe of diameter D, given that diameter of venturi throat = diameter of orifice opening.
- Give two industrial applications of:
(i) packed beds

(ii) fluidized beds - Differentiate between aggregative and particulate fluidization.
- (a) By applying momentum balance to the steady flow of a fluid in a stream-tube, derive Eulers equation of motion. (8)

(b) Obtain Bernoulli equation from Euler equation by making necessary assumptions. (4)**Or** - For laminar flow of a Newtonian fluid in circular pipe, obtain the following relations from first principles:
(i) Frictional pressure drop and wall shear stress

(ii) Velocity distribution in the radial direction

(iii) Average velocity and maximum velocity

(iv) Pressure drop and average velocity

- Water is pumped from a ground level reservoir to an overhead tank through a 7.5 cm ID pipe as shown in the sketch:
(a) What pressure is needed at the outlet of the pump to supply water to the tank at the rate of 100 ltr/min? Data:

(b) What is the power required for the pump, if the pump is only 60% efficient?

m = 1 cP; r = 1 g/ml.

Equivalent length of fittings (L_{e}/D):

Globe valve (open) : 300

45^{o}elbow : 15

Fanning friction factor for turbulent flow is given by: f = 0.079 (NRe)^{-0.25} -
(a) A venturi meter has throat to upstream pipe cross-section ratio of 0.5.
The fluid flowing is water. The pressure at the entry of converging cone
section is 137.9 kN/m
^{2}(a). What is the velocity at the throat which corresponds to a pressure of 0 kN/m^{2}(a) at the throat? If the water is at 200^{o}F, what is the highest velocity possible at the throat at which water will boil?

Data: For water at 200^{o}F,

Density = 980 kg/m^{3}. Vapor pressure = 75.8 kN/m^{2}(a). (8)(b) A rotameter with a stainless steel float has a maximum capacity of 1.2 ltr/sec of water. What will be the maximum capacity for kerosene in ltr/sec for the same rotameter and float? Assume that the C

_{d}for the rotameter is not changing much with flowrate.

Data:

Specific gravity of stainless steel = 7.92

Specifc gravity of kerosene = 0.82 (4) - (a) Derive relations for Reynolds number and friction factor and
establish the Ergun equation for single-phase flow of fluid through
packed bed. (8)

(b) Bring out the equation predicting minimum fluidization velocity. (4) - A mixture of vapors pass through a packed bed of glass spheres having density 2.4 g/cc each
of diameter 0.5 cm. The pressure drop due to the flow is 4000 N/m
^{2}. The height of packed bed is 1.85 m. The density and viscosity of the vapor mixture are 3.8 x 10^{-3}g/cc and 0.015 cP respectively.

Data:

Cross sectional area of the packed column tube = 0.09 m^{2}

Bed porosity = 0.4Find the mass flow rate of the vapor mixture.