22-Mec-B2 Environmental Control in Buildings · December 2017

Question 7 of 8: Centrifugal fan selection from a manufacturer’s table

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. Engineers Canada national examination 16-Mec-B2 Environmental Control in Buildings, December 2017, three hours, open book. Eight problems of 20 points each; candidates are required to solve five, and all questions carry the same value. ASHRAE Psychrometric Chart No. 1 (SI and inch-pound) and a pressure–enthalpy diagram for R-717 are appended to the paper as pages 6–8.

All eight problems are worked here. The paper mixes SI and inch-pound units deliberately: Problems 1, 3 and 4 are SI, Problems 2, 6 and 7 are inch-pound, and Problem 8 is SI with a Canadian climate. Each solution is worked in the units the question uses, as the cover-page instructions require.

Reference texts for this subject.

W. P. Jones, Air Conditioning Engineering, 5th ed., Butterworth-Heinemann — the standard reference for this examination code; Ch. 2–3 (psychrometry and the psychrometric chart), Ch. 6 (air-conditioning plant cycles), Ch. 7 (the cooling coil, apparatus dew point and by-pass factor), Ch. 9 (cooling towers), Ch. 15 (fans).
McQuiston, Parker & Spitler, Heating, Ventilating and Air Conditioning: Analysis and Design, 6th ed., Wiley — Ch. 3 (moist air), Ch. 5 (heat transmission in building structures), Ch. 8 (energy estimating and the degree-day method), Ch. 12 (fans and duct design).
ASHRAE Handbook — Fundamentals — Ch. 1 (psychrometrics), Ch. 14 (climatic design information), Ch. 21 (duct design), Ch. 25–27 (thermal and moisture performance of the building envelope), Ch. 30 (fenestration).
Stoecker & Jones, Refrigeration and Air Conditioning, 2nd ed., McGraw-Hill — Ch. 10–12 (vapour-compression cycle, compressors, condensers and evaporators); ASHRAE Handbook — Refrigeration for ammonia plant practice.
National Building Code of Canada and the National Energy Code of Canada for Buildings (NRC), Appendix C climatic data; CSA and Canada Green Building Council material for Problem 5.

Property basis used throughout. Moist-air properties are computed from the ASHRAE Fundamentals ideal-moist-air relations, so every state quoted here can be read back off the psychrometric chart supplied with the paper:

$$W=\frac{0.621945\,p_w}{p-p_w},\qquad h_{\text{SI}}=1.006\,t+W\,(2501+1.86\,t),\qquad h_{\text{IP}}=0.240\,t+W\,(1061+0.444\,t)$$

with $h$ in $\text{kJ/kg}$ of dry air for $t$ in $\,{}^{\circ}\text{C}$ and in $\text{Btu/lb}$ of dry air for $t$ in $\,{}^{\circ}\text{F}$. Ammonia properties are quoted on the same datum as the attached ASHRAE p–h diagram ($h_f=200\ \text{kJ/kg}$ and $s_f=1.0\ \text{kJ/(kg}\cdot\text{K)}$ for saturated liquid at $0\,{}^{\circ}\text{C}$); only differences enter the answers, so any consistent chart or table gives the same duties.

Question 7: Centrifugal fan selection from a manufacturer’s table (20 points)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The duty is $12{,}000\ \text{cfm}$ at $1.25\ \text{in w.g.}$ static. The relevant part of the manufacturer’s table is the $1\text{-}1/4$ in static-pressure column, which brackets the required flow:

CFM	VEL (ft/min)	RPM at $1\text{-}1/4$ in sp	BHP at $1\text{-}1/4$ in sp
$11{,}172$	$1200$	$474$	$2.97$
$12{,}000$ (required)	$1235$	?	?
$12{,}103$	$1300$	$483$	$3.22$

Find. The rotational speed and shaft power at the duty point, and the fan and system characteristics plotted at that speed.

Approach. Interpolate linearly within the $1\text{-}1/4$ in column, which is legitimate because the tabulated points are close together and the fan characteristic is smooth between them; then verify the selection against the table’s own notes and construct the two curves.

Part (a) — interpolate for the speed. The required $12{,}000\ \text{cfm}$ lies between the $11{,}172$ and $12{,}103\ \text{cfm}$ rows: $$f=\frac{12{,}000-11{,}172}{12{,}103-11{,}172}=\frac{828}{931}=0.8894$$ $$N=474+0.8894\,(483-474)=482.0 \;\Rightarrow\;\boxed{N\approx482\ \text{rpm}}$$
Part (b) — interpolate for the power. Using the same fraction on the brake-horsepower column: $$\text{BHP}=2.97+0.8894\,(3.22-2.97)=3.19 \;\Rightarrow\;\boxed{3.19\ \text{hp}=2.38\ \text{kW}}$$ The table note warns that BHP excludes drive loss; at a typical belt-drive efficiency of $95\%$ the motor must deliver $3.36\ \text{hp}$, so a $5\ \text{hp}$ frame is the selection. Check it against the table’s own limit: the maximum BHP at this speed is $31.14\,(482/1000)^2=7.23\ \text{hp}$, so the fan is running at $44\%$ of its non-overloading limit and cannot overload the motor anywhere on its curve.

Confirm the selection against the remaining table notes. Three independent checks, all of which the table invites:

Check	Relation	Value
Tip speed	$10.537\times482$	$5079\ \text{ft/min}$ — modest, so noise and wheel stress are not issues
Inlet velocity	$12{,}000/9.72$	$1235\ \text{ft/min}$ — matches the tabulated VEL of $1200$–$1300$, confirming the row
Air power	$Q\,p_s/6356=12{,}000(1.25)/6356$	$2.36\ \text{hp}$
Static efficiency	$2.36/3.19$	$\mathbf{73.9\%}$ — near the peak of the fan, so the selection is a good one

The fan characteristic at $482\ \text{rpm}$. The table gives the fan at many different speeds, so every entry must be transposed to the selected speed by the fan laws before it can be plotted as one curve: $$\frac{Q_2}{Q_1}=\frac{N_2}{N_1},\qquad \frac{p_2}{p_1}=\left(\frac{N_2}{N_1}\right)^{2},\qquad \frac{P_2}{P_1}=\left(\frac{N_2}{N_1}\right)^{3}$$ Applying this to each tabulated point gives the characteristic below. That the transposed points from different pressure columns all fall on one smooth curve is itself the proof that the fan laws hold and that the interpolation is sound:

Table entry	At $482\ \text{rpm}$: $Q$ (cfm)	$p_s$ (in w.g.)	BHP
$10{,}241$ cfm @ $466$ rpm, $1\text{-}1/4$ in	$10{,}593$	$1.337$	$3.04$
$11{,}172$ cfm @ $474$ rpm, $1\text{-}1/4$ in	$11{,}361$	$1.293$	$3.12$
$12{,}103$ cfm @ $483$ rpm, $1\text{-}1/4$ in	$12{,}078$	$1.245$	$3.20$
$13{,}034$ cfm @ $494$ rpm, $1\text{-}1/4$ in	$12{,}717$	$1.190$	$3.29$
$13{,}965$ cfm @ $506$ rpm, $1\text{-}1/4$ in	$13{,}303$	$1.134$	$3.36$
$11{,}172$ cfm @ $510$ rpm, $1\text{-}1/2$ in	$10{,}559$	$1.340$	$3.03$
$7448$ cfm @ $360$ rpm, $3/4$ in	$9972$	$1.344$	$2.88$

The system characteristic. A fixed duct system is a turbulent-flow resistance, so its pressure loss varies as the square of the flow: $$p_s=p_{s,\text{design}}\left(\frac{Q}{Q_{\text{design}}}\right)^{2} =1.25\left(\frac{Q}{12{,}000}\right)^{2}$$ giving $0.31$ in at $6000$ cfm, $0.56$ at $8000$, $0.87$ at $10{,}000$, $1.25$ at $12{,}000$ and $1.70$ at $14{,}000\ \text{cfm}$. The operating point is where this parabola cuts the fan curve, and the plot below confirms that the two intersect at the required duty — which is the graphical statement that the selection is correct.

The fan characteristic transposed to 482 rpm (red, open circles are transposed table entries) and the system parabola (blue). They intersect at the required 12,000 cfm / 1.25 in w.g.

Final results.

Quantity	Result
(a) Rotational speed	$\mathbf{482\ \text{rpm}}$
(b) Shaft power (BHP, excluding drive loss)	$\mathbf{3.19\ \text{hp}=2.38\ \text{kW}}$
Motor selection at $95\%$ drive efficiency	$3.36\ \text{hp}$ → $5\ \text{hp}$ frame
Tip speed	$5079\ \text{ft/min}$
Maximum BHP at this speed	$7.23\ \text{hp}$ (fan is non-overloading)
Inlet velocity	$1235\ \text{ft/min}$
Air power / static efficiency	$2.36\ \text{hp}$ / $73.9\%$
System curve	$p_s=1.25\,(Q/12{,}000)^2$

Check: two corrupt cells in the printed table. Transposing every entry in the table to $482\ \text{rpm}$ by the fan laws should collapse the whole table onto a single characteristic, and it very nearly does. Two cells fall conspicuously off it: the $10{,}241\ \text{cfm}$ row shows $438\ \text{rpm}$ in the $7/8$ in column, out of order in a sequence reading $300,\ 321,\ 341,\ 363,\ 385,\ \mathbf{438},\ 427$, where about $406$ is required; and the $9310\ \text{cfm}$ row shows $361\ \text{rpm}$ in the $5/8$ in column against a required $350$. Both are digit errors in the printed table, not properties of the fan. Neither touches this answer, which is interpolated between the $11{,}172$ and $12{,}103\ \text{cfm}$ rows of the $1\text{-}1/4$ in column, and both are excluded from the plotted characteristic. The check is worth running on any selection made from tabulated data: a manufacturer’s data set that does not collapse under the fan laws contains a misprint.

Topic. Fan selection, the fan laws and the system characteristic.

Key relations. Fan laws at constant diameter and density: $Q\propto N$, $p\propto N^2$, $P\propto N^3$. System resistance: $p\propto Q^2$. Air power (inch-pound): $\text{ahp}=Q\,p_s/6356$ for $Q$ in cfm and $p_s$ in in w.g.; static efficiency $\eta_s=\text{ahp}/\text{BHP}$. Operating point: the intersection of the fan curve at its running speed with the system parabola.

Why this works. A fan does not have an operating point of its own — it has a characteristic, and the duct system it is connected to has another, and the machine runs where the two cross. That is why a fan cannot be selected on flow alone, and why changing the system (closing a damper, fouling a filter) moves the operating point along the fan curve rather than simply reducing the flow proportionally. The fan laws follow from geometric similarity: at fixed diameter, blade velocities scale with speed, so flow scales with speed, the velocity pressure it can develop scales with speed squared, and power — the product of the two — scales with speed cubed. The cube law is the single most useful fact in ventilation energy work: trimming a fan by $20\%$ in speed halves its power, which is the entire economic case for variable-speed drives on variable-air-volume systems.

Common pitfall. Interpolating across static-pressure columns instead of within one. Each column is a different operating condition, and the tabulated speeds are not linear across them; the interpolation must be made within the column that matches the required static pressure, along the flow direction. The second common error is quoting BHP as the motor size: the table note is explicit that BHP excludes drive loss, so the motor must be sized above it, and above the non-overloading maximum if the system resistance is uncertain.

Source. Jones, Air Conditioning Engineering, 5th ed., Ch. 15 (fans, fan laws and fan/system matching); ASHRAE Handbook — Systems and Equipment, Ch. 21; McQuiston, Parker & Spitler, 6th ed., §12-5 to §12-8.

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