Air at 20ºC and 1 atm flows at 5 m/s past a flat plate. At x = 60 cm and y = 2.95 mm, use the Blasius solution to find the following. Determine the wall shear stress at the specified location.
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Air at $20^{\circ} \mathrm{C}$ and 1 atm flows at $5 \mathrm{m} / \mathrm{s}$ past a flat plate. At $x=$ $60 \mathrm{cm}$ and $y=2.95 \mathrm{mm},$ use the Blasius solution, Table $7.1,$ to find $(a)$ the velocity $u ;$ and $(b)$ the wall shear stress. (c) For extra credit, find a Blasius formula for the shear stress away from the wall.
Maitreya E.
Flow of air develops in a horizontal cylindrical duct, of diameter $D=15$ in., following a well-rounded entrance. A turbulent boundary grows on the duct wall, but the flow is not yet fully developed. Assume that the velocity profile in the boundary layer is $u / U=(y / \delta)^{1 / 7} .$ The inlet flow is $U=50 \mathrm{ft} / \mathrm{s}$ at section ?. At section ? , the boundary-layer thickness is $\delta_{2}=4$ in. Evaluate the static gage pressure at section ? located at $L=20$ ft. Find the average wall shear stress.
In turbulent flow past a flat surface, the velocity $u$ near the wall varies approximately logarithmically with distance $y$ from the wall and also depends upon viscosity $\mu,$ density $\rho,$ and wall shear stress $\tau_{w} .$ For a certain airflow at $20^{\circ} \mathrm{C}$ and 1 atm, $\tau_{w}=0.8 \mathrm{Pa}$ and $u=15 \mathrm{m} / \mathrm{s}$ at $y=3.6 \mathrm{mm} .$ Use this information to estimate the velocity $u$ at $y=6 \mathrm{mm}$
Hunza G.
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