Problem 2.1:
Air enters a tank at a velocity of
m/s
and leaves the tank at a velocity of
m/s.
If the flow is adiabatic find the difference between the temperature of the air at exit and the temperature
of the air at inlet.
Solution:
Given: \( V_{1}=100\,\text{m/s} \), \( V_{2}=200\,\text{m/s} \).
To calculate: \( T_{2}-T_{1}=? \)
The schematic diagram of the problem description is shown in Fig. 1.
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Using the conservation of energy, \[ c_{p}T_{1}+\frac{V_{1}^{2}}{2}+\frac{\dot{q}}{\dot{m}}=c_{p}T_{2}+\frac{V_{2}^{2}}{2} \]
\[
1005\times T_{1}+\frac{100^{2}}{2}+\cancelto{\text{adiabatic}}{\frac{\dot{q}}{\dot{m}}}=1005\times
T_{2}+\frac{200^{2}}{2}
\]
The solution for \( T_{2}-T_{1} \) can be obtained as,
\[
T_{2}-T_{1}=\frac{100^{2}-200^{2}}{2\times1005}
\]
\[
\boxed{T_{2}-T_{1}=-14.92537^{\circ}\text{C}}
\]