Problem 1.6:
Two air streams are mixed in a chamber. One stream enters the chamber through a
cm diameter
pipe at a velocity of
m/s
with a pressure of
kPa
and a temperature of
oC.
The other stream enters the chamber through a
cm diameter
pipe at a velocity of
m/s
with a pressure of
kPa
and a temperature of
oC.
The air leaves the chamber through a
cm
diameter pipe at a pressure of
kPa
and a temperature of
oC.
Assuming that the flow is steady, find the velocity in the exit pipe.
Solution:
Given: Steady flow
The schematic diagram of the problem description is shown in Fig. 1.
The densities of air at the various stations may be calculated using the respective pressures, temperatures and using the ideal gas equation.
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Using the conservation of mass equation,
$$\begin{aligned} m_{1}+m_{2} &= m_{3} \\ \rho_{1}\,A_{1}\,V_{1}+\rho_{2}\,A_{2}\,V_{2} &= \rho_{3}\,A_{3}\,V_{3} \\ \rho_{1}\times\frac{\pi}{4}D_{1}^{2}\times V_{1} + \rho_{2}\times\frac{\pi}{4}D_{2}^{2}\times V_{2} &= \rho_{3}\times\frac{\pi}{4}D_{3}^{2}\times V_{3} \end{aligned}$$