ME2135 QUIZ_February 2010

25 February 2010 Metric Number:___________ Number:________________ _____

Department of Mechanical Engineering National University of Singapore

ME 2135 – Fluid Mechanics II– Quiz – Dr Dilip A Shah Time Allocated: 1 Hour

Instructions to Candidates: 1. Answer ALL questions. 2. This quiz is equivalent to 10% of the course total score. 3. Enter only your metric number on the top right corner of this page.

Q.1 The stream function ψ for a two-dimensional potential flow is given by the expression: ψ  = K θ  − C ln r 

where K = 4 m 2/s and C = 6 m 2/s. (i) Determine the velocity at point P which is located at (x,y) = (5,6). (ii) What is the value of stream function at P? (iii) If the pressure at point P is 4.8 Pa, what is the pressure at point (2,3)? You may take the density ρ = 1.2 kg/m 3. In Polar coordinates, u ’ and v’ are related to stream function ψ in the following manner: u

'

=

1 ∂ψ  r 

∂θ 

and 

v

'

=−

∂ψ  ∂r 

.

(35 marks)

Q.2 Consider the centrifugal pump running at a fixed rotation rate and having the characteristic curve:  H P

=

 H 0

−

2

CQ .

 A single or a combination of these pumps are to be applied in series to pump a liquid in a system with the system characteristic curve given as:  H S 

=

 z 0

+

KQ

2

(i) Express the flow rate Q (in terms of H 0, C, z0 and K) obtained with the two such identical pumps in series. (ii) If H0 = 2 z0  and K = 2 C, how much more flow rate is generated using 2 pumps in series versus only one pump. (iii) How much more head is developed by two pumps in series as compared to one pump?

(50 marks)

Q.3 The stream function in an incompressible flow is given by Ψ = x2 – 2y2. Calculate the circulation around a closed path joined by straight lines in sequence between the points (-1,0), (1,0), (1,1) and (-1,1). You may use: u=

∂ψ  ∂ y

and 

v=−

∂ψ 

.

∂ x

(15 marks)