Question

A viscous fluid flows past a flat plate such that the boundary layer thickness at a distance 1.2 m from the leading edge is 11 mm. Determine the boundary layer thickness at distances of (a) 0.3 m, (b) 3.0 m, (c) 30.0 m from the leading edge. Assume laminar flow.

Answer 1

Answer:

(a) when the distance x is 0.3 m, the boundary layer thickness is 0.0055 m = 5.5 mm.

(b) when the distance x is 3 m, the boundary layer thickness is 0.0174 m = 17.4 mm.

(c) when the distance x is 30 m, the boundary layer thickness is 0.055 m = 55 mm.

Explanation:

For a laminar flow:

$d = C\sqrt{x}$  ;

where;

d is the boundary layer thickness = 11 mm

x is the distance from the leading edge = 1.2 m

C is a constant =?

$C = \frac{d}{\sqrt{x}} = \frac{11 X 10^{-3}}{\sqrt{1.2}} = 0.010042$

Part (a): when x = 0.3m

d = C√x

  = 0.010042 × √0.3

  = 0.0055 m = 5.5 mm

Part (b): when x = 3.0 m

d = C√x

  = 0.010042 × √3.0

  = 0.0174 m = 17.4 mm

Part (c): when x = 30 m

d = C√x

  = 0.010042 × √30

  = 0.055 m = 55 mm