Question

Consider air flowing with a velocity of 70 m/s flowing over a flat plate. The local convection heat transfer coefficient can be correlated by Nux = 0.03Re0.8Pr1/3 . Assuming air is at 1 atm pressure and using its properties at 20◦C, calculate the friction coefficient and wall shear stress at 2 m from the leading edge of the plate.

Answer 1

Answer:

The coefficient of friction at 2m from leading edge is 0.00243

Explanation:

Given that,stream velocity(V)=70m/s

Obtaining properties of air at 20°C,we get

Density is

$ρ = 1.204kgm {}^{ - 3}$

Kinematic Viscosity is

$v = 1.516 \times 10 {}^{ - 5} m {}^{2} s {}^{ - 1}$

Calculating reynolds Number at location 2m from edge of the plate as follows

$Re _{x} = \frac{Vx}{v}$

Therefore,

$Re _{x} = \frac{70 \times 2}{1.516 \times 1 0{}^{ - 5} } = 9.235 \times 10 {}^{6}$

The relation for Nusselt Number is given as follows in the question

$Nu = 0.03Re _{x} {}^{0.8} Pr {}^{ \frac{1}{3} }$

The relation for stanton number is given as

$St _{x} = \frac{Nu}{Re _{x} Pr} \\ hence \: St _{x} = \frac{0.03Re _{x} {}^{0.8} Pr {}^{ \frac{1}{3} } }{Re _{x} Pr} \\ = 0.03Re _{x} {}^{ - 0.2} Pr {}^{ \frac{2}{3} }$

The relation for coefficient of friction from Chilton colburn analogy is given as

$\frac{C _{f,x}}{2} = St _{x}Pr {}^{ \frac{2}{3 } } \\ = > \frac{C _{f,x}}{2} = 0.03Re _{x} {}^{ - 0.2} Pr {}^{ \frac{ - 2}{3} } Pr {}^{ \frac{2}{3 } } \\ = > C _{f,x} = 0.06Re _{x} {}^{ - 0.2}$

Substituting value of reynold's number we get

$C _{f,x} = 0.06(9.235 \times 10 {}^{6} ) {}^{ - 0.2} \\ = 0.00243$

Therefore,the coefficient of friction at 2m from leading edge is 0.00243

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