Derive Prandtl’s universal velocity distribution equation for turbulent flow in pipes. What do you understand by velocity defect?

(10 Marks) May-2018

Subject Fluid Mechanics 2

Topic Turbulent Flow

Difficulty Medium

1) $\tau = \rho l^2 (\frac{du}{dy})^2$ from this equation, the velocity distribution can be obtained if the relation between L, the mixing length and y is known.

2) Pranditl assumed that mixing length, L is linear function of the distance y from the pipe wall. i.e., L = Ky where …