Question

A space 2.5cm wide between two large plane surfaces is filled with oil.Force required to drag a very thin plate of area 0.5m2 just midway the surfaces at a speed of 0.5m/s is 1n . Then find coefficient of viscocity

Answer 1

Given : A space 2.5cm wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area 0.5m² just midway the surfaces at a speed of 0.5m/s is 1N.

To find : The coefficient of viscosity.

solution : here velocity gradient, dv/dz

= (0.5 m/s)/(2.5/2 × 10¯² m)

= 40 sec¯¹

here viscous force applied on the plate is from upper as well as lower portion of the oil. and also both are equal.

so formula of viscous force is...

$F_{viscous}=\eta 2A\frac{dv}{dz}$

here $F_{viscous}$ = 1N , A = 0.5 m² , dv/dz = 40

⇒1 = η × 2 × 0.5 × 40

⇒η = 1/40 = 2.5 × 10¯² Kgs/m²

Therefore the coefficient of viscosity is 2.5 × 10¯² kgs/m²