Question

If in a turbulent boundary layer the velocity distribution is assumed to be given by $u\propto y^{1/4}$, then the boundary layer thickness varies with longitudinal distance X as

• A. $X^{1/2}$
• B. $X^{1/7}$
• C. $X^{1/3}$
• D. $X^{4/5}$

Answer 1

The correct option is D $X^{4/5}$

$Forvelocitydistributionu\propto y^{1/4},theexpressionforboundarylayerthicknessisgiven$

$=\frac{0.37x}{(R{e}_x{)}^{1/5}}$

$R{e}_x=\frac{vx}{\nu }$

$\delta =K{x}^{4/5}$

$\delta \propto x^{4/5}$