Question

Steam enters a one-inlet, two-exit control volume at location (1) at 360°C, 100 bar, with a mass flow rate of 2 kg/s. The inlet pipe is round with a diameter of 5.2 cm. Fifteen percent of the flow leaves through location (2) and the remainder leaves at (3). For steady-state operation, determine the inlet velocity, in m/s, and the mass flow rate at each exit, in kg/s.

Answer 1

Answer:

The inlet velocity is 21.9 m/s.

The mass flow rate at reach exit is 1.7 kg/s.

Explanation:

Given that,

Mass flow rate = 2 kg/s

Diameter of inlet pipe = 5.2 cm

Fifteen percent of the flow leaves through location (2)  and the remainder leaves at (3)

The mass flow rate is

$m_{2}=0.15\times2$

We need to calculate the mass flow rate at reach exit

Using formula of mass

$m_{3}=m_{1}-m_{2}$

$m_{3}=2-0.15\times2$

$m_{3}=1.7\ kg/s$

We need to calculate the inlet velocity

Using formula of velocity

$v=\dfrac{m}{\rho A}$

Put the value into the formula

$v=\dfrac{2}{42.868\times\dfrac{\pi}{4}\times(5.2\times10^{-2})^2}$

$v=21.9\ m/s$

Hence, The inlet velocity is 21.9 m/s.

The mass flow rate at reach exit is 1.7 kg/s.