Problem 2.3:
Air being released from a tire through the valve is found to have a temperature of
oC.
Assuming that the air in the tire is at the ambient temperature of
oC,
find the velocity of the air at the exit of the valve. The process can be assumed to be adiabatic.
Solution:
Given:
T1=30oC = 303
K,
V1= 0 m/s,
T2=15oC = 288
K,
adiabatic flow \( \implies\dot{q}=0 \).
To calculate: V2=?
The schematic diagram of the problem description is shown in Fig. 1.
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Using the conservation of energy, \[ c_{p}T_{1}+\frac{V_{1}^{2}}{2}+\frac{\dot{q}}{\dot{m}}=c_{p}T_{2}+\frac{V_{2}^{2}}{2} \]
\[
1005\times303+\frac{0^{2}}{2}+\cancelto{\text{adiabatic}}{\frac{\dot{q}}{\dot{m}}}=1005\times288+\frac{V_{2}^{2}}{2}
\]
The solution for V2 can be obtained as,
\[
V_{2}=\sqrt{2\times1005\times\left(303-288\right)}
\]
\[
\boxed{V_{2}=173.64\,\text{m/s}}\ .
\]