A thin plate 6 ft long and 3 ft wide is submerged and held stationary in a stream of water (T = 60°F) that has a velocity of 17 ft/s. What is the thickness of the boundary layer on the plate for Rex = 500,000 (assume that the boundary layer is still laminar), and at what distance downstream of the leading edge does this Reynolds number occur? What is the shear stress on the plate at this point?

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cjmejiab cjmejiab · Answer 1 · 2019-11-01T21:19:16+01:00

A) In the case of the Boundary Thickness Layer we use the given formula,

[tex]\delta = \frac{4.91x}{\sqrt{Re}}[/tex]

We know as well that,

Re = Número de Reynolds = [tex]\frac{U*x}{\upsilon}[/tex]

Where,

U = velocity

[tex]\upsilon[/tex] = kinematic viscosity

For water, kinematic viscosity, [tex]\upsilon = 1.21*10^{-5} ft^2 /s[/tex]

So, [tex]500,000 = \frac{ 17x}{(1.21*10^{-5})}[/tex]

[tex]x = 0.355 ft[/tex]

[tex]d = \frac{4.91*0.355}{\sqrt {500000}}[/tex]

[tex]d = 0.002465 ft = 0.029in[/tex]

B) For flat plate boundary layer. Given the Critical Reynolds Number.= 5*10^5 we know that is equal to Re above.

Thus, [tex]x = 0.355 ft[/tex]

C. Wall shear stress,

[tex]\tau = \mu*\sqrt{ U^3 / (2*\nu*x) }[/tex]

For water, dynamic viscosity, [tex]\nu[/tex] = 2.344*10^-5 lbf-s/ft^2

[tex]\tau = 2.344*10^-5 \sqrt {17^3 / (2*1.21*10^{-5}*0.355)}[/tex]

[tex]\tau = 0.5605 lbf/ft^2[/tex]