If the upper plate moving at 1.1 m/s with respect to lower plate is stationary and pressure difference between the two sections 60m apart is 60$kN/m^{2}$, determine:

i. Velocity distribution

ii. Discharge per unit width, and

iii. Shear stress on the upper plate

Given: $μ = 0.88 poise = 0.088 Ns/ m ^2$ (Viscosity of the fluid)

h = 10 mm (gap between the two horizontal plates)

U = 1.1 m/s (Relative velocity of the upper plate with respect to the lower plate

$∆P=60 kN/ m ^2$ (Pressure difference between two sections)

∆x=60 m (Distance between sections)"

To find: Velocity distribution (u)

Discharge per unit width (q)

Shear stress on the upper plate (τ)

Sol:

We know from the definition of the problem that the flow is a couette flow,

∴q = $4.553x10^{-3} m^3$/s per unit width

Shear Stress on the upper plate is,

$\tau=μ \frac{du}{dy}$ at y=h

Now,

$\frac{du}{dy}=\frac{d}{dy}$ [5681.818y(y-0.01)+110y]

∴$\frac{du}{dy}$=[5681.818(2y-0.01)+110]

At y=h

$\frac{du}{dy}$=166.818 /sec

∴$\tau=μ \frac{du}{dy}$=0.088(166.818)

∴$\tau=14.68 N/m^2$