Two parallel plates kept 10cm apart have laminar flow of oil between them with a maximum velocity of 2m/s. Calculate.

i) The discharge per meter width

ii) The shear stress at the plate.

iii) The difference in pressure between two points 20 m apart.

iv) The velocity gradient at the plates.

v) The velocity at 20 mm from plate. Assume viscosity of oil as 20 poise.

Given :

$u_{\text {max }}=2 \mathrm{~m}/\mathrm{s}$

$u_{\text {avg }}=\frac{2}{3}u_{\text {max }}=1.334 \mathrm{~m} / \mathrm{s}$

$D=100mm$

$\mu =20 Poise = 2Pa.sec$

(1 Poise = 0.1 Pa.sec = 0.1 Ns/m²)

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(a) Discharge per unit width

$\begin {aligned} Q &= Area \times Velocity_{avg}\\ &=D \times 1 \times u_{avg}\\ &= 0.1 \times …