A sphere is placed in an air stream that is at atmospheric pressure and moving at 30 m/s. Using the density of air constant at 1.23 kg/m^3, calculate (a) the stagnation pressure and (b) the pressure on the surface of the sphere at a point B, 24°C from the stagnation point, if the velocity there

Question

A sphere is placed in an air stream that is at atmospheric pressure and moving at 30 m/s. Using the density of air constant at 1.23 kg/m³, calculate (a) the stagnation pressure and (b) the pressure on the surface of the sphere at a point B, 24°C from the stagnation point, if the velocity there is 67 m/s.

Accepted Answer

(a) Applying the expression given in the preceding problem, we obtain

[latex] p_{S}=p_{0}+\frac{1}{2} ho V_{0}^{2}=101,400+\left(\frac{1}{2} ight)(1.23)(30)^{2}=102,000 Pa =102.0 kPa [/latex].

[latex] ext { (b) The specific weight of air }= ho g=(1.23)(9.81)=12.1 N / m ^{3} [/latex].

Applying the Bernoulli equation, stagnation point to point B, produces

[latex]\left(\frac{p_{S}}{\gamma}+\frac{V_{S}^{2}}{2 g}+0 ight)-0=\left(\frac{p_{B}}{\gamma}+\frac{V_{B}^{2}}{2 g}+0 ight) \quad ext { or } \quad\left(\frac{102,000}{12.1}+0+0 ight)=\left(\frac{p_{B}}{\gamma}+\frac{(67)^{2}}{2 g}+0 ight)[/latex].

[latex] ext { from which } p_{B} / \gamma=8200 m ext { of air, and } p_{B}=\gamma h=(12.1)(8200)=99,200 Pa =99.2 kPa[/latex].

Question 7.38: A sphere is placed in an air stream that is at atmospheric p...

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