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Question 10

10.(a)  If n identical water droplets falling under gravity with terminal velocity v collides to form a single drop which has the terminal velocity 4v, find the number n.

(b)  If the velocity of water near the surface of a 6 m deep river is 6 m/s, assuming uniform velocity gradient along the depth, find the shear stress between the horizontal layers of water ( coefficient of viscosity of water = 10-2 poise ).

 

yu
  • -19
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b)
shear stress= tangential force per unit area. so,
A=1 m2 
coefficient of viscosity of water = 10-2 poise =10-4 kg/ms
dv=6m/s
dz=6m
shear stress=(10-4 kg/ms * 1 m2  * 6m/s) / 6 m = 10-4 kgms-2
 
  • 4
a)
the terminal velocity(v) is directly proportional to the square of the radius of the drop.
R3  = nr3
R = cube root of nr3
v/4v = r2/n3/2 r2 
n3/2 = 4
n=8
  • 2
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