Question

If the velocity profile of a fluid over a flat plate is parabolic with free stream velocity of 120 cm/s occurring at 20 cm from the plate. Find the velocity gradient and shear stress at a distance of 10 cm from plate. dynamic viscosity = 8.5 Poise

Answer 1

$$u=ay^2+by+c\\c=0\\120=1(20)^2+b(20)\\\frac{du}{dy}=40a+b\\u=-0.3y^2+12y$$

a)

$$\frac{du}{dy}=-0.3(10)+12=6\ s^{-1}$$

b)

$$\tau=6(0.85)=5.1\ Pa$$