Question

Suppose a fluid whose coefficient of viscosity is η and density ρ, flows through a cylindrical tube of radius r and length L. Let P be the pressure difference in the liquid at both ends of the tube. If the volume of the liquid flowiing per unit time through the cylindrical tube depends on the pressure gradient P/L, the coefficient of viscosity η and radius r, obtain an expression for the volume of liquid flowing per unit time through the tube. [Take k = π/8]​

Answer 1

Answer

Correct option is

B

8

1

The r be the radius,L be the length and P is the pressure difference.Generally the Q is represented as rate of flow of liquid but here it is taken as V, Therefore V=

ηl

πQpr

4

As for now V=Q

Now using the Poiseuille equation for the rate of flow of liquid.

Which is V=πΔPr

4

/8lη

Comparing with the above equation of V,

So on comparing we get the value of Q=1/8

Hope it helps