## Related questions with answers

Performance data for a centrifugal fan of 3-ft diameter, tested at 750 rpm, are

$\begin{matrix} \text{Volume flow rate Q (}{\mathrm{ft}^{3} /s)} & \text{106} & \text{141} & \text{176} & \text{211} & \text{246} & \text{282}\\ \text{Static pressure rise, }{\Delta p} (psi) & \text{0.075} & \text{0.073} & \text{0.064} & \text{0.050} & \text{0.033} & \text{0.016}\\ \text{Power output }{\mathscr{P} (hp)} & \text{2.75} & \text{3.18} & \text{3.50} & \text{3.51} & \text{3.50} & \text{3.22}\\ \end{matrix}$

Plot the performance data versus volume flow rate. Calculate static efficiency, and show the curve on the plot. Find the best efficiency point, and specify the fan rating at this point. Using the fan, determine the minimum size square sheet-metal duct that will carry a flow of 200 $\mathrm{ft}^{3}$/s over a distance of 50 ft. Estimate the increase in delivery if the fan speed is increased to 1000 rpm.

Solution

Verified**Given:**

Data of the centrifugal fan are given:

System geometric parameters are:

$\begin{aligned} n&=750 \hspace{0.1cm} \text{rpm}\\ Q&=200 \hspace{0.1cm} \frac{\text{ft$^3$}}{\text{s}} \\ n'&=1000 \hspace{0.1cm} \text{rpm}\\ D&=3\hspace{0.1cm} \text{ft}\\ L&=50\hspace{0.1cm} \text{ft}\\ \rho_{air}&=0.00237 \hspace{0.1cm} \frac{\text{slug}}{\text{ft$^3$}}\\ \nu_{air}&=1.58 \cdot 10^{-6} \hspace{0.1cm} \frac{\text{ft$^2$}}{\text{s}}\\ \end{aligned}$

**Find:**
Calculate the minimum size square duct for the given flow rate and distance. Calculate minimum size square duct for increased fan speed.

**Assumptions and principles:**
It is assumed that the roughness of the duct is neglected as well as the minor and major losses (Only losses due friction are active).

It is assumed that ducting is smooth and that roughness of the duct is neglected.

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