EMH102 FLUID MECHANICS
TUTORIAL 7
1.
The drag force FD on a very rough sphere held inside a pipe in which liquid is flowing is
a function of D, ρ, , V, and k, D is the diameter of the sphere, ρ is mass density,  is
viscosity, V, is the velocity of the liquid, and k is the height of the roughness elements on
the sphere.
By dimensional analysis, determine the relevant dimensionless numbers for this problem.
Express your answer in the functional form
FD
 f  1 ,  2 
V 2 D 2
2.
Starting with the functional relationship ΔP = f (ρ, L, V, , Ev, , ∆) show by the
exponent method that
 LV
P
V
LV 2 V 2  


f
,
,
,
 

L 
V 2
Ev / 

3.
An experimental test program is being set up to calibrate a new flowmeter. The flow
meter is to measure the mass flow rate of rate of liquid flowing through a pipe. It is
assumed that the mass flow rate is a function of the following variable:
m  f P, D,  ,  
.
Where ∆P is the pressure difference across the meter, D is the pipe diameter,  is the
liquid viscosity, and ρ is the liquid density. Using dimensional analysis, find the groups. Express your answer in the form:
.
m
PD
4.
2
 f  
A ¼ scale model of an experimental bathysphere that will operate at great depths is tested
to determine its drag characteristic by towing it behind a submarine. For true similitude,
what should be the towing speed relative to the speed of the prototype?
(4VP)
5.
Using the Reynolds-number criterion, a 1:1 scale model of a torpedo is tested in a wind
tunnel. If the velocity of the torpedo in water is 10 m/s. what should be the air velocity
(standard atmospheric pressure) in the wind tunnel? The temperature for both tests is
10ºC.
(107.6m/s)