KVPY2015PhysicsMechanical Properties of Fluids
Stoke's law states that the viscous drag force F experience by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity , is given by F=6 n a v If this fluid is flowing through a cylindrical pipe of radius r , length 1 and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as v t =k ( p l )^ a ^ b r^ c Where
Options
- Aa =1, ~b =-1, c =4
- Ba =-1, ~b =1, c =4
- Ca =2, ~b =-1, c =3
- Da =1, ~b =-2, c =-4
Correct answer
A. a =1, ~b =-1, c =4
Step-by-step solution
array l V t = ( p l )^ a ^ b r^ c L³ T⁻¹= (M L⁻² T⁻² )^ a L^ c (M L⁻¹ T⁻¹ )^ b a + b =0 -2 a-b+c=3 -2 a-b=-1 c=4, a=1, b=-1 array Ans (A) is correct