Correct Answer - Option 4 : shows increasing fullness with increase in Reynolds number
Explanation:
Velocity distribution in turbulent through the smooth pipe is given as:
\(\frac{{̅ U}}{{{U_*}}} = 5.75{\log _{10}}\left( {\frac{{{U_*}R}}{ν }} \right) + 1.75\)
\(\frac{U}{{{U_*}}} = 5.75{\log _{10}}\left( {\frac{{{U_*}y}}{ν }} \right)\)
Where, U* = Shear or friction velocity, y = distance from the pipe wall, ν = kinematic viscosity of the fluid
From the equation, it is clear that, as Reynold's number increases, U̅ Increases
Velocity Distribution for Turbulent Flow in pipes.
Prandtl’s universal velocity distribution equation.
\(v = {v_{max}} + 2.5{V^*}{\log _e}\left( {\frac{y}{R}} \right)\)
Where, \({V^*} = \sqrt {\frac{{{\tau _0}}}{\rho }} = Shear\;or\;friction\;velocity.\)
y = distance from the pipe wall
ρ = Density of fluid.
On observing the above equation we can say that velocity distribution in the turbulent boundary layer follows logarithmic law and dependent on the Reynolds number.
