The velocities of cylindrical layers of liquid flowing through a tube , situated at distances 0.8cm and 0.82cm from the axis of the tube are 3cms^(-1)and2.5cms^(-1)respectively . Find the viscous force acting between these layers , if the length of the tube is 10 cm and the coefficient of viscosity of the liquid is 8 poise .

The velocities of cylindrical layers of liquid flowing through a tube

1.	The velocities of cylindrical layers of liquid flowing through a tube , situated at distances 0.8cm and 0.82cm from the axis of the tube are 3cms^(-1)and2.5cms^(-1)respectively . Find the viscous force acting between these layers , if the length of the tube is 10 cm and the coefficient of viscosity of the liquid is 8 poise .
Answer» Solution :`r_(1)=0.8cm,r_(2)=0.82cm` `DELTAV=3-2.5=0.5cms^(-1)` `Deltax=` DISTANCE between the layers `=0.02cm` `L=10cm` A = AREA of CONTACT of two layers `=2pi((r_(1)+r_(2))/(2))L` `eta=8`poise Now `F_(v)=etaA(Deltav)/(Deltax)` `=eta[2pi(r_(1)+r_(2))/(2)L](Deltav)/(Deltax)` `=8[2xx3.14((0.8+0.82)/(2))10](0.5)/(0.02)` `=16xx3.14xx0.81xx10xx25` `F_(v)=10173.6` dyne