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ES3C9
FLUID MECHANICS FOR MECHANICAL ENGINEERS
Example Class 5
(1) A coastal power plant takes in cooling water through a vertical perforated
manifold, as in figure 1. The total volume flow Q past the manifold, as shown.
Estimate (a) how far downstream and (b) how far normal to the paper the
effects of the intake are felt in the ambient 8m deep waters.
Fig 1:
Q
110

 2.19m 2 s 1 (lecture 14)
2 b 16
m 2.19

 8.75m (lecture 15)
Then the stagnation point is at a 
U  0.25
And L  2 a  55m
a    
(Stagnation line r 
, so when   0 and r   then r sin    a )
sin 
The sink strength is m 
(2) Effect of mirror design on the fuel consumption of a car
As part of the continuing efforts to reduce the drag coefficient and thus to improve the
fuel efficiency of cars, the design of side rear-view mirrors has changed drastically
from a simple circular plate to a streamlined shape. Determine the amount of fuel and
money saved per year as a result of replacing a 13cm diameter flat mirror (CD =1.1)
by one with a hemispherical back (CD=0.4) (figure 2). Assume the car is driven
L=24000 km a year at an average speed of 95km/h. Take the density and price of
gasoline to be 0.8kg/L and £0.80/L, respectively; the heating value (HV) of gasoline
to be 44000 kJ/kg and the overall efficiency of the engine to be ηcar =30%. The effect
of the car body on the flow around the mirror is negligible (no interference). The air
density is 1.2kg/m3.
Fig 2:
The drag force acting on a body is F  CD A
body. So for both mirrors, A 
V 2
2
, where A is the frontal area of the
 D2
. Then FD-flat =6.1 N.
4
Over one year, the work of the drag is W D-flat =F D-flat *L=146000kJ/year.
The energy required for one year is : Ein= W D-flat / ηcar=488000kJ/year.
m fuel Ein / HV 488000 / 44000


 13.9 L / year
Amount of fuel V fuel  flat 
 fuel
 fuel
0.8
Cost flat =13.9*0.8=£11.12 /year
The drag and the work done to overcome are directly proportional to the drag
coefficient. Then the percent reduction in the fuel consumption due to replacing the
mirror is equal to the percent reduction in the drag coefficient:
CD _ flat  CD _ hemi
 0.636
CD _ flat
Fuel reduction = 0.636*13.9=8.84L/year
Reduction ratio =
Cost reduction = 0.636*11.12=£7.07/year
Since a typical car has two mirrors, the driver saves more than £14 per year in
gasoline by replacing the flat mirrors with hemispherical ones.