When a viscous liquid flow, adjacent layers opposes their relative motion by applying a viscous force given by
F = – η A 
Where,
η = Coefficient of viscosity
A = Surface area of adjacent layers in contact
= Velocity gradient
If such type of a viscous liquid having density ρ of coefficient of viscosity η is flowing through a fixed tube of length λ and radius r under a pressure difference of P between the two ends of tube, then the rate of volume flow of liquid per second through the tube is given by Poiseuillis equation that is
Q = 
(i) The pressure difference P at the ends of tube is constant then velocity at axis of tube is –
Text Solution
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Ans.
(i)
Sol. Consider a cylindrical volume of liquid of radius x. Due to steady flow net force on the liquid in cylindrical volume is zero.
– η 2 π x λ 
= P π x 2 
∴ v = v 0 
where v 0 = 
(ii)
Sol. Sol. Consider a cylindrical volume of liquid of radius x. Due to steady flow net force on the liquid in cylindrical volume is zero.
– η 2 π x λ 
= P π x
2 
∴ v = v 0 
where v 0 = 
(iii)
Sol. Sol. Consider a cylindrical volume of liquid of radius x. Due to steady flow net force on the liquid in cylindrical volume is zero.
– η 2 π x λ 
= P π x
2 
∴ v = v 0 
where v 0 = 
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