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Refrigeration and Air Conditioning

W F Stoecker

Chapter 6

Fan and Duct Systems - all with Video Answers

Educators

Chapter Questions

01:02

Problem 1

Compute the pressure drop of $30^{\circ} \mathrm{C}$ air flowing with a mean velocity of $8 \mathrm{~m} / \mathrm{s}$ in a circular sheet-metal duct $300 \mathrm{~mm}$ in diameter and $15 \mathrm{~m}$ long, using (a) Eqs. (6-1) and (6-2) and (b) Fig. 6-2. Ans. (a) $36 \mathrm{~Pa}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
04:02

Problem 2

A pressure difference of $350 \mathrm{~Pa}$ is available to force $20^{\circ} \mathrm{C}$ air through a circular sheet-metal duct $450 \mathrm{~mm}$ in diameter and $25 \mathrm{~m}$ long. Using Eq. (6-1) and Fig. 6-1, determine the velocity. Ans. $25.6 \mathrm{~m} / \mathrm{s}$

Supratim Pal
Supratim Pal
Numerade Educator
01:33

Problem 3

A rectangular duct has dimensions of 0.25 by $1 \mathrm{~m}$. Using Fig. 6-2, determine the pressure drop per meter length when $1.2 \mathrm{~m}^3 / \mathrm{s}$ of air flows through the duct. Ans. $0.65 \mathrm{~Pa} / \mathrm{m}$

James Kiss
James Kiss
Numerade Educator
03:01

Problem 4

A sudden enlargement in a circular duct measures $0.2 \mathrm{~m}$ diameter upstream and $0.4 \mathrm{~m}$ diameter downstream. The upstream pressure is $150 \mathrm{~Pa}$ and downstream is 200 $\mathrm{Pa}$. What is the flow rate of $20^{\circ} \mathrm{C}$ air through the fitting? Ans. $0.467 \mathrm{~m}^3 / \mathrm{s}$

Anand Jangid
Anand Jangid
Numerade Educator
01:01

Problem 5

A duct $0.4 \mathrm{~m}$ high and $0.8 \mathrm{~m}$ wide, suspended from a ceiling in a corridor, makes a right-angle turn in the horizontal plane. The inner radius is $0.2 \mathrm{~m}$, and the outer radius is $1.0 \mathrm{~m}$, measured from the same center. The velocity of air in the duct is $10 \mathrm{~m} / \mathrm{s}$. To how many meters of straight duct is the pressure loss in this elbow equivalent? Ans. $15 \mathrm{~m}$.

Raj Bala
Raj Bala
Numerade Educator
03:01

Problem 6

An 0.3 - by $0.4-\mathrm{m}$ branch duct leaves an 0.3 - by $0.6-\mathrm{m}$ main duct at an angle of $60^{\circ}$. The air temperature is $20^{\circ} \mathrm{C}$. The dimensions of the main duct remain constant following the branch. The flow rate upstream is $2.7 \mathrm{~m}^3 / \mathrm{s}$, and the pressure is $250 \mathrm{~Pa}$. The branch flow rate is $1.3 \mathrm{~m}^3 / \mathrm{s}$. What is the pressure $(a)$ downstream in the main duct and (b) in the branch duct? Ans. (a) $346 \mathrm{~Pa},(b) 209 \mathrm{~Pa}$

Anand Jangid
Anand Jangid
Numerade Educator
05:41

Problem 7

In a branch entry, an airflow rate of $0.8 \mathrm{~m}^3 / \mathrm{s}$ joins the main stream to give a combined flow rate of $2.4 \mathrm{~m}^3 / \mathrm{s}$. The air temperature is $25^{\circ} \mathrm{C}$. The branch enters with an angle $\beta=30^{\circ}$ (see Fig. 6-12). The area of the branch duct is $0.1 \mathrm{~m}^2$, and the area of the main duct is $0.2 \mathrm{~m}^2$ both upstream and dow-stream. What is the reduction in pressure between points $u$ and $d$ in the main duct? Ans. $95 \mathrm{~Pa}$

Chai Santi
Chai Santi
Numerade Educator
03:01

Problem 8

A two-branch duct system of circular duct is shown in Fig. 6-20. The fittings have the following equivalent length of straight duct: upstream to branch, $4 \mathrm{~m}$; elbow, $2 \mathrm{~m}$. There is negligible pressure loss in the straight-through section of the branch. The designer selects $4 \mathrm{~Pa} / \mathrm{m}$ as the pressure gradient in the 12 - and $15-\mathrm{m}$ straight sections. What diameter should be selected in the branch section to use the available pressure without dampering? Ans. $0.35 \mathrm{~m}$

Anand Jangid
Anand Jangid
Numerade Educator
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Problem 9

A duct system consists of a fan and a $25-\mathrm{m}$ length of circular duct that delivers $0.8 \mathrm{~m}^3 / \mathrm{s}$ of air. The installed cost is estimated to be $$\$ 115$$ per square meter of sheet metal, the power cost is 6 cents per kilowathour, the fan efficiency is 55 percent, and the motor efficiency 85 percent. There are $10,000 \mathrm{~h}$ of operation during the amortization period. Assume $f=0.02$. What is the optimum diameter of the duct? Ans. $0.24 \mathrm{~m}$

Victor Salazar
Victor Salazar
Numerade Educator
03:19

Problem 10

Measurements made on a newly installed air-handling system were: $20 \mathrm{r} / \mathrm{s}$ fan speed, $2.4 \mathrm{~m}^3 / \mathrm{s}$ airflow rate, $340 \mathrm{~Pa}$ fan-discharge pressure, and $1.8 \mathrm{~kW}$ supplied to the motor. These measurements were made with an air temperature of $20^{\circ} \mathrm{C}$, and the motor. These measurements were math air at a temperature of $40^{\circ} \mathrm{C}$. If the fan speed remains at $20 \mathrm{r} / \mathrm{s}$, what will be the operating values of $(a)$ airflow rate, $(b)$ static pressure, and $(c)$ power? Ans. (c) $1.685 \mathrm{~kW}$
(GRAPH CANT COPY)

Narayan Hari
Narayan Hari
Numerade Educator
03:35

Problem 11

A fan-duct system is designed so that when the air temperature is $20^{\circ} \mathrm{C}$, the mass flow rate is $5.2 \mathrm{~kg} / \mathrm{s}$ when the fan speed is $18 \mathrm{r} / \mathrm{s}$-and the fan motor requires $4.1 \mathrm{~kW}$. A new set of requirements is imposed on the system: the operating air temperature is changed to $50^{\circ} \mathrm{C}$, and the fan speed is increased so that the same mass flow of air prevails. What are the revised fan speed and power requirement? Ans. $19.8 \mathrm{r} / \mathrm{s}, 4.95 \mathrm{~kW}$

Dading Chen
Dading Chen
Numerade Educator
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Problem 12

An airflow rate of $0.05 \mathrm{~m}^3 / \mathrm{s}$ issues from a circular opening in a wall. The centerline velocity of the jet is to be reduced to $0.75 \mathrm{~m} / \mathrm{s}$ at a point $3 \mathrm{~m}$ from the wall. What should be the outlet velocity $u_o$ of this jet? Ans. $1.84 \mathrm{~m} / \mathrm{s}$

Rashmi Sinha
Rashmi Sinha
Numerade Educator
06:54

Problem 13

Section 6-19 points out that jets entrain air as they move away from their inlet into the room. The entrainment ratio is defined as the ratio of the air in motion at a given distance $x$ from the inlet to the airflow rate at the inlet $Q_x / Q_o$. Use the expression for the velocity in a circular jet, Eq. (6-32), multiplied by the area of an anular ring $2 \pi r d r$ and integrate $r$ from 0 to $\infty$ to find the expression for $Q_x / Q_o$. Ans. $0.405 x /$ $\sqrt{A_o}$

Satpal Satpal
Satpal Satpal
Numerade Educator
03:52

Problem 14

From the equation for velocities in a plane jet, determine the total included angle between the planes where the velocities are one-half the centerline velocities at that $x$ position. Ans. $13.2^{\circ}$

Supratim Pal
Supratim Pal
Numerade Educator