Question 8.3: Two infinite plates are h distance apart as in Fig. 8.10. Th...

Two infinite plates are h distance apart as in Fig. 8.10. There is a fluid of viscosity \mu between the plates and the pressure is constant. The upper plate is moving at speed U = 4 m/s. The height of the channel h = 1.8 cm. Calculate the shear stress at the upper and lower walls if \mu=0.44 \mathrm{~kg} / \mathrm{m} . \mathrm{s} and \rho=888 \mathrm{~kg} / \mathrm{m}^{3} .

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Re =\rho h U / \mu=(888)(1.8 / 100)(4) / 0.44=145 . So, the flow is laminar and \tau=\mu \frac{\partial u}{\partial y}, u at any is given by \frac{U}{h} y .

Shear stresses at the two walls are of equal magnitude, therefore,

\tau =\mu \frac{\partial u}{\partial y}=\mu \frac{(U-0)}{h}=(0.44)(4) /(1.8 / 100)  

= 97.8 Pa

 

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