# UPTU Old Question Papers

# B Tech 8th Semester

# Advanced Fluid Mechanics 2007

Notes : (1) Attempt all the five questions.

(2) All questions carry equal marks.

(3) Use of gas / air tables to permitted.

**1. Attempt any four of the following :**

(a) Discuss Reynolds transport theorem in brief.

(b) Explain what do you understand by total acceleration, local acceleration and convective acceleration for any fluid flow field.

(c) Explain wall shear in brief.

(d) Explain rotation and linear translation motion of a fluid particle.

(e) Determine the velocity and acceleration of fluid particle at (2, 3, 4) and t = 0.2 for the velocity field given by U = 10x^{2}z + 15x y j +100 t h VB-4061]

2. Attempt any four of the following :

(a) The following velocity components for steady, incompressible flow describe the fluid motion o 2,22 _{A}, 2 u = zx -xy + z , v = x – 4xy + y , w = 2xy – yz + y^{2,} whether the continuity equation is satisfied.

(b) Explain briefly the doublet

(c) Explain circulation and its theorem.

(d) What do understand by Rankine body ? Draw stream lines to deposit a Rankine body.

(c) Explain Euler’s equation and its significance.

(f) The stagnation points are located at -31.5° and -148.5° angular position on the periphery of a cylinder having 50 cm diameter rotating at some speed in the uniform flow of 15 m/s. Determine the speed of rotating cylinder.

**3. Answer any two of the following :**

(a) The velocity distribution in the boundary layer is given by

/ \ | r \ | |

y | i | |

UJ | 2 | UJ |

determine the expressions for boundary layer thickness, wall shear stress and coefficient of drag in terms of Reynold’s number.

(b) Stating assumptions derive Hagen-Poisenelle equation for laminar flow. Also derive expressions for shear stress and velocity distribution.

(c) Write short notes on any two of the following :

(1) Boundary layer separation and its control

(2) Plane couette flow

(3) Development of boundary layer

**4. Answer any two of the following :**

(a) Explain Mach number, Mach time and Mach cone. Derive energy equation and describe various regions of flow.

(b) Air flows from a reservoir

(p_{0} = 1 MN/m^{2} and T_{Q} = 40° C) through delaval nozzle with a throat diameter of 0.1m and a maximum Mach number of 0.75. Calculate the mass flow rate, nozzle diameter, velocity pressure and temperature at the exit where

M = 0.50

(c) Show that the non-dimensional impulse function

displacement and momentum thickness.

* can be given as below for isentropic flow with variable area :

**5. Answer any two of the following :**

(a) Obtain relationships among the various thermodynamic properties for a Rayleigh process and explain Rayleigh live also.

(b) Air flows from a reservoir at standard conditions through a convergent – divergent nozzle to constant cross-section pipe. Assuming the mass flow rate from the reservoir to the Fanno flow system is 55.8 kg/m^{2}s, construct a T-S diagram under Fanno flow condition.

(c) Write short notes on any two of the following :

(i) shock waves

(ii) wind tunnel

(iii) Fannolines / curve and its importance.