Question

Air enters a 28-cm diameter pipe steadily at 200 kPa and 20°C with a velocity of 5 m/s. Air is heated as it flows and leaves the pipe at 180 kPa and 40 °C. Determine the mass flow rate of air and the velocity at the exit.

Answer 1

Answer:

The mass flow rate of air is 0.732 kg/s.

The velocity at the exit is 5.927 m/s.

Explanation:

Given that,

Diameter = 28 cm

Enter pressure= 200 kPa

Enter temperature = 20°C

Velocity = 5 m/s

Exit pressure = 180 kPa

Exit temperature = 40°C

We need to calculate the mass flow rate of air

Using formula of mass flow rate

$\dot{m}=\rho\times \dot{V}$

$\dot{m}=\dfrac{P}{RT}\times A\times v$

Put the value into the formula

$\dot{m}=\dfrac{200}{0.287\times293}\times\dfrac{(0.28)^2}{4}\times\pi\times5$

$\dot{m}=0.732\ kg/s$

We need to calculate the volume flow rate

Using formula of volume flow rate

$\dot{V'}=\dfrac{\dot{m}}{\rho'}$

$\dot{V'}=\dfrac{RT'\dot{m}}{P'}$

$\dot{V'}=\dfrac{0.287\times313\times0.732}{180}$

$\dot{V'}=0.365\ m^3/s$

We need to calculate the velocity at the exit

Using formula of velocity

$v'=\dfrac{\dot{V'}}{A}$

Put the value into the formula

$v'=\dfrac{4\times0.365}{(0.28)^2\times\pi}$

$v'=5.927\ m/s$

Hence, The mass flow rate of air is 0.732 kg/s.

The velocity at the exit is 5.927 m/s.