**Anna University, B.TECH DEGREE **

**( CHEMICAL ENGINEERING) ( 5 ^{th }SEMESTER)**

**FLUID MECHANICS**

**PART – A ( 10 X 2 = 20 Marks)**

1. When do you prefer an inclined manometer ?

2. accum gage reads 10 in. Hg when the atmospheric pressure is 30 in. Hg. Assuming the density of mercury to be 13 . 595 kg / m^{3} ^{, }determine the pressure in Pascal.

3. ine the following dimensionless numbers:

(i) Weber number (ii) Froude Number, (iii) Euler’s Number

4. Explain geometric similarity, kinematic similarity and dynamic similarity.

5. Distinguish between Laminar and turbulent flow.

6. Distinguish between kinetic energy correction factor and momentum correction factor.

7. Define sphericity factor.

8. Water is flowing in two different pipes of diameters ‘d’ and ‘D’ . Sketch the friction factor vs Reynolds Number for the two cases.

9. Define hydraulic radius and equivalent diameter.

10. Why is there a negative sign in the pressure – height relation?

# PART – B ( 5 X 16 = 80 Marks)

11.The density of a sample of cement is found to be 3100 kg/m^{3}. 25.4 gm of this cement is packed into a column of diameter = 2.50 cm to form a bed of 27.3 cm thick. When a pressure drop of 12.5 cm of Hg is established across the bed, it is found that 774 secs. are required to drive 250 c m^{3 }of air through the bed.

Calculate the average diameter of particles in the cement (assuming spherical) and the surface area per gram of cement.

Data : µ_{air = }1.83 X 10^{-5} kg / m – sec^{2 }?Hg = 1.355 X 10^{4 }kg/m3

^{ }g = 9.81 m/sec^{2}

12. (a) A uniform film of oil 0.13mm thick separates two dics, each of 200mm diameter, mounted coaxially. Ignoring edge effects, calculate the torque necessary to rotate one disc relative to other at a speed of 7 revolutions/sec., if the oil has viscosity of 0.14 Pascal – sec.

**(OR)**

(b) Compute the atmospheric pressure at elevation 6000m, for the two cases listed below. Considering the atmosphere as a static fluid.

Case (i) Constant temperature between sea level and 6000m and

Case (ii) air temperature decreasing linearly with elevation at a standard rate of

0.0065º c/m.

Data : At sea level T = 15ºc P = 100 KN/m^{2}? = 12.03 N/m^{3}

13. (a) Bring out the importance of the relation between the shear stress and velocity

gradient in characterizing the behaviour of flowing fluids.

(b) Water at room temperature flows through a smooth straight pipe A of internal diameter 4cm at an average velocity of 42 cm/sec. Oil flows through another pipe B of internal diameter 12.5 cm at such a velocity that dynamic similarity exists between the two streams. Calculate the velocity through pipe B. (Specific Gravity of oil = 0.85, viscosity of oil = 2 cp and viscosity of water = 1 cp.)

**(OR)**

(c ) Derive Bernoulli’s equation for flow through a straight pipe.

(d ) Explain the significance of each term in the above equation

14. (a) Derive Hagen Poisuille equation for pressure drop in laminar flow.

**(OR)**

The power required by an agitator in a tank is a function of the following four Variables : (a) diameter of the impeller, (b) RPM of the impeller, (c ) viscosity of liquid, (d) density of liquid and acceleration due to gravity (g)

From the dimensional analysis, obtain a relation between power and the variables. The power of consumption is found, experimentally, to be proportional to the square of the speed of rotation.

(a) A two dimensional fluid motion is specified in the Legrandian manner by the equation x = x_{0 }e^{kt} , y = y_{0} e^{-kt}

(1) find the path of fluid particle

(2) the expression for velocity in the Eulerian form

(3) state whether the motion is steady and

(4) whether it is kinematically possible for an incompressible fluid

**(OR)**

(b) For the velocity profile u= u_{max } ( I – r/r_{w}) ^{1/n }compute the kinetic energy correction factor and momentum correction factor. What are the values when n = 7?