A large room uses a fan to draw in atmospheric air at 20°Cthrough a 30-cm by 30-cm commercial-steel duct 12 mlong, as in Fig. . Estimate (a) the airflow rate in m3/hif the room pressure is 10 Pa vacuum and (b) the roompressure if the flow rate is 1200 m3/h. Neglect minor losses. 30 cm by 30 cmRoomFanPatm12 m

(a) The density of the air is: ρair=1.2kgm3 For commercial steel, ε=0.046 mm Side length, DH=30 cm…

Answered: 30 cm by 30 cm Room Fan Patm 12 m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A large room uses a fan to draw in atmospheric air at 20°C
through a 30-cm by 30-cm commercial-steel duct 12 m
long, as in Fig. . Estimate (a) the airflow rate in m³/h
if the room pressure is 10 Pa vacuum and (b) the room
pressure if the flow rate is 1200 m³/h. Neglect minor losses.

Expert Solution

Step 1

(a) The density of the air is: $ρ_{a i r} = 1.2 \frac{k g}{m^{3}}$

For commercial steel, $ε = 0.046 m m$

Side length, $D_{H} = 30 c m$

The viscosity of air is, $μ = 1.8 \cdot 10^{- 5} \frac{k g}{m \cdot s}$

The value of change in pressure is, $∆ P = 10 P a (v a c c u m)$ .

Now use the formula, $∆ P = \frac{ρ f L V^{2}}{2 D_{H}}$ and simplify to calculate the value of velocity ' $V$ '.

$\begin{array}{rcl} ∆ P & = & \frac{ρ f L V^{2}}{2 D_{H}} \\ 10 & = & \frac{1.2 \cdot 0.0190 \cdot 12 \cdot V^{2}}{2 \cdot 0.3} \\ V & = & 4.69 \frac{m}{s} \end{array}$

Step 2

Now the value of flow rate is calculated by using the formula, $Q = A V$ and substitute $V = 4.69 \frac{m}{s}$

$\begin{array}{rcl} Q & = & A V \\ = & 0.3 \cdot 0.3 \cdot 4.69 \\ = & 0.4221 \frac{m^{3}}{s} \\ = & 0.4221 \cdot 3600 \frac{m^{3}}{h} \\ = & 1519.56 \frac{m^{3}}{h} \end{array}$

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