**GTU previous years question papers**

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**BE SEM-III Examination May 2012**

**Subject code: 130101**

**Subject Name: Fluid Mechanics**

** **

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**Q.1 (a) **(i) What is the difference between dynamic viscosity and kinematic viscosity? State their units.

(ii) Obtain an expression for capilari rise of liquid? **04**

**(b) **Calculate the pressure exerted by 5 kg of nitrogen gas at a temperature of 10ºc if the volume is 0.4cubic meter. Molecular weight of nitrogen is 28.Assume ideal gas laws are applicable. take universal gas constant (MR) = 8314 Nm/kg-mole-K

**Q.2 (a) **(i) What is compressibility? Derive an expression for it ?

(ii) Describe vertical single column manometer? How will you measure the fluid pressure with it ?

**(b) **Determine the total pressure on a circular plate of diameter 1.5 m which

is placed vertically in water in such a way that the centre of the plate is 3 m below the free surface of water. Find the position of centre of pressure also.

**OR**

**(b) **A pontoon of 15696 KN displacement is floating in water a weight of 245.25 KN is moved through a distance of 8 m across the deck of pontoon which tilts the pontoon through an angle of 4° find the metacentric height of the pontoon.

**Q.3 (a) **(i) Define the terms metacentre, metacentric height and absolute pressure.

(ii) What do you mean by equipotential line and a line of constant stream function?

**(b) **An open circular cylinder of 15 cm diameter and 100 cm long contains water up to a height of 80 cm. Find the maximum speed at which the cylinder is to be rotated about its vertical axis so that no water spills.

**OR**

**Q.3 (a) **(i) State Bernoulli’s theorem.

(ii) Derive an expression for the discharge through a ventureimeter.

**(b) **A horizontal Venturimeter with inlet diameter 20cm and throat diameter 10cm is used to measure the flow of oil of sp.gr 0.8. The discharge of oil through venturimeter is 60 Liters/Second. Find the reading of the oil mercury differential manometer take Cd = 0.98.

**Q.4 (a) **(i) What are the advantages of triangular notch over rectangular notch ?

(ii) Find an expression for the discharge over a rectangular notch.

**(b) **Derive an expression for Hagen Poiseuille’s theorem.

**OR**

**Q.4 (a) **(i) Define Kinetic Energy correction factor and momentum correction factor.

(ii) Show that the value of the co-efficient of friction for viscous flow through a circular pipe is given by f =- 16/Re where Re = Reynolds number.

**(b) **Explain Dash pot mechanism and its utility.

**Q.5 (a) **(i) What is meant by geometric, kinematic , and dynamic similarities?

(ii) State Buckingham’s Π theorem method.. What do you mean by repeating variables

**(b) **Calculate the stagnation pressure temp. and density on the stagnation point on the nose of the plane which is flying at 800 km/hr through still air having a pressure 8 N/square cm (abs) and temp. – 10 º c. Take R =

287 J/Kg –K, γ = 1.4

**OR**

**Q.5 (a) **(i) Define Mach Number and Mach cone

(ii) Prove that the velocity of sound waves in a compressible fluid is given by

C = √ (k/ρ).

K= Bulk modulus.

ρ = Mass Density.

**(b) **Derive and expression for area velocity relation ship for a compressible fluid in the form with usual notation

dA/A= (dV/V)[M³-1]

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