Given:
- the velocity of water in the river is 5m/s at the surface
- The viscosity of water is 10^-3
- The river is 5m deep
To find: what is viscous forces per unit area between a horizontal layer of water?
Explanation:
as we know that,
velocity at the bottom of the river will be zero,
Velocity gradient,
= dv/dy
= 18×[tex]10^{3} [/tex]/60×60×5
= 1[tex]s^{-1} [/tex]
Now,
The viscous force,
F = ηA[tex]\frac{dv}{dY} [/tex] is tangential to the area
by using the formula of Shear stress,
= F/A
= η[tex]\frac{dv}{dY} [/tex]
= [tex]10^{-3} [/tex]×1
= [tex]10^{-3} [/tex] [tex]\frac{N}{m^{2} } [/tex]
Hence the viscous force is [tex]10^{-3} [/tex] [tex]\frac{N}{m^{2} } [/tex]