Question

The 48-W fan of a central heating system is to circulate air through the ducts. The analysis of the flow shows that the fan needs to raise the pressure of air by 50 Pa to maintain flow. The fan is located in a horizontal flow section whose diameter is 30 cm at both the inlet and the outlet. Determine the highest possible average flow velocity in the duct. (Round the final answer to one decimal place.)

Answer 1

3.39 m/s

Step-by-step explanation:

The fan need to maintain a pressure (p) of 50 Pa, also the power = 48 W.

The surface area of the duct (A) is given as:

`A=\pi D^2\\\\But\ D=diameter =30cm=0.3m\\\\Hence:\\\\A=\pi(0.3)^2=0.283\ m^2`

The mass flow rate is given by the formula:

`P=\dot{m}.(p)/(\rho)\\ \\m=(P*\rho)/(p)\\ \\`

The velocity (V) in the duct can be calculated from the formula:

`\dot{m}=\rho*V*A\\\\V=\frac{\dot{m}}{\rho*A}\\ \\Substituting\ \dot{m}=(P*\rho)/(p)\\ \\V=((P*\rho)/(p))/(\rho *A)\\ \\V=(P)/(p*A)\\ \\V=(48)/(50*0.283)=3.39\\ \\V=3.39\ m/s`