A large closed tank is filled with ammonia under a pressure of 5.30 psi gage and at 65°F. The ammonia discharges into the atmosphere through a small opening in the side of the tank. Neglecting friction losses, calculate the velocity of the ammonia leaving the tank assuming (a) constant density and

Question

A large closed tank is filled with ammonia under a pressure of 5.30 psi gage and at 65°F. The ammonia discharges into the atmosphere through a small opening in the side of the tank. Neglecting friction losses, calculate the velocity of the ammonia leaving the tank assuming (a) constant density and (b) adiabatic flow conditions.

Accepted Answer

(a) Apply the Bernoulli equation, tank to atmosphere.

[latex]\left(\frac{5.30 imes 144}{\gamma_{1}}+0+0 ight)=\left(0+\frac{V^{2}}{2 g}+0 ight)[/latex].

[latex] ext { where } \gamma_{1}=\frac{p_{1}}{R T}=\frac{(5.30+14.7)(144)}{(89.5)(460+65)}=0.0613 lb / ft ^{3}[/latex].

Substituting and solving, V = 895 ft/sec.

For a constant specific weight γ, either gage or absolute pressure heads may be used. Absolute pressure head must be used for cases where γ is not constant.

[latex] ext { (b) For } V_{1}=0 ext { and } z_{1}=z_{2} ext {, }[/latex]the adiabatic expression (D) in Problem 7.21 may be written

[latex]\left(\frac{k}{k-1} ight)\left(\frac{p_{1}}{\gamma_{1}} ight)\left[1-\left(\frac{p_{2}}{p_{1}} ight)^{(k-1) / k} ight]=\frac{V_{2}^{2}}{2 g}[/latex].

For ammonia, k = 1.32 from Table 1 in the Appendix, and

[latex]\frac{1.32}{0.32} imes \frac{20.0 imes 144}{0.0613}\left[1-\left(\frac{14.7 imes 144}{20.0 imes 144} ight)^{0.242} ight]=\frac{V_{2}^{2}}{2 g} \quad ext { or } \quad V_{2}=947 ft / sec[/latex].

The error in using the velocity based upon the constant density assumption is about 5.3%.
The specific weight of the ammonia in the jet is calculated by using the expression

[latex]\frac{p_{1}}{p_{2}}=\left(\frac{\gamma_{1}}{\gamma_{2}} ight)^{k} \quad ext { or } \quad \frac{20.0}{14.7}=\left(\frac{0.0613}{\gamma_{2}} ight)^{1.32} ext { and } \gamma_{2}=0.0485 lb / ft ^{3}[/latex].

Despite this 20.7% change in density, the error in the velocity was only 5.3%.

Question 7.39: A large closed tank is filled with ammonia under a pressure ...

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