Anewtonian fluid is placed in a slit of thickness, h, between two flat, plates that are horizontal to gravity. the upper plate moves at velocity u parallel to the lower plate, which is stationary. find the velocity profile in the slit.

Proof with Explanation:

From the Newton's law of viscosity we have

where is the wall shear stress

is the coefficient of dynamic viscosity

is the velocity gradient in the flow

Now from the principle of boundary layer condition we know that the velocity of the fluid that is in contact with a surface the velocity of the fluid is same as that of the boundary itself.

Hence from the attached figure we can infer that

Velocity at

Velocity at

Solving equation 'i' we get

from the boundary conditions we obtain that c = 0 since

Also we have

spectral lines lyman is one set

vapour or gas assuming atmospheriv pressure