King Saud University
College of Engineering
Mechanical Engineering Department
ME 381: FLUID MECHANICS
First Semester Second Examination (1427/1428 H) time: 50 minutes
Question 1
(a) A u component of velocity is given by u = A xy , where A is a constant. What is a possible incompressible? What must the v component if the flow is v component be if the flow is irrotational?
(b) The velocity along the centerline of a nozzle is given by the following expression:
Where V r
V r
=
2 t x
(1 )
2
2 L i r the velocity in meter per second, t is time in seconds, x is distance along the nozzle, and L is the length of nozzle and equal to 1 m. Determine the local and convective accelerations when
L x =
2 and t = 3 seconds.
(c) A two-dimensional flow field is defined by u = xt + 2 y and v = xt
2
yt . What is the acceleration at a point x = 1 m, y = 1 m, and at time t = 1 s? Is the flow rotational or irrotational?
Question 2
(a) Body A travels in through water at a constant speed of 12 m/s.
Velocities at points B and C are induced by the moving body are observed to have magnitudes of 4 m/s and 2 m/s, respectively. What is P
B
P
C
?
(b) Air (

= 1.2 Kg/m 3 ) flows past a wing section with uniform velocity of 50 m/s. The velocities at points on top and bottom of the wing

section are 95 m/s and 75 m/s, respectively. Compute the pressure difference between the bottom and top of this wing section.
Question 3
(a) Water (

= 1000 Kg/m 3 and

= 0.001 kg/m-s) flows through a 25-cm smooth pipe at the rate of 0.05 m 3 /s. What is the friction factor f ?
What is the friction factor f if the pipe is made of cast iron?
(b) Kerosene (

= 820 Kg/m 3 and

= 0.0015 kg/m-s) flows at the rate of
0.03 m 3 /s in a 20-cm pipe. Would you expect the flow to be laminar or turbulent? And why?
(c) Flow of a liquid in a smooth 3-cm pipe is found to yield a head of 1 m per meter of pipe when the average velocity is 1 m/s. If the rate of flow were doubled, would the head loss also doubled? And why?
(d) Oil (

= 850 Kg/m 3 and

= 0.510 kg/m-s) flows in a 5-cm smooth pipe at a rate of 0.250 m 3 /s. What is the head loss per 100 m of length of pipe?
Question 4
(a) Determine the dimensions of the following variables and combinations of variables in terms of the length, mass, and time. i.
ii.
T (Torque).
2 r V
, where V is velocity and r is density.
2 iii.
t / r , where t is shear stress. iv.
Q / D
3 w , where Q is discharge (flow rate), D is diameter, and w is angular velocity
(a) It is well known that for flow past cylinders, vortices are alternately shed from one side of the cylinder and the other. The frequency of shedding n , is a function of the approach velocity V , the diameter D of the cylinder, the density r , and the viscosity m . Using V , r , and D as repeated parameter, determine the dimensionless parameters for this phenomenon.