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Q12PE

Expert-verifiedFound in: Page 428

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**The main uptake air duct of a forced air gas heater is 0.300 m in diameter. What is the average speed of air in the duct if it carries a volume equal to that of the house’s interior every 15 min? The inside volume of the house is equivalent to a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high.**

**The average air speed in duct is \({\bf{10}}{\bf{.33}}\;{\bf{m/s}}\).**

**Given Data:**

**The diameter of air duct is \(d = 0.3\;{\rm{m}}\)**

**The time to fill the room by gas is \(t = 15\;\min = 900\,{\rm{s}}\)**

**The size of house is \(V = 13\;{\rm{m}} \times 20\;{\rm{m}} \times 2.75\;{\rm{m}}\)**

**The average speed of air in duct is found by dividing the volume of house by time and area of air duct.**

**The area of the air duct is given as:**

**\(A = \frac{\pi }{4}{d^2}\)**

**Substitute all the values in the above equation.**

**\(\begin{aligned}A &= \frac{\pi }{4}{\left( {0.3\;{\rm{m}}} \right)^2}\\A &= 0.071\;{{\rm{m}}^2}\end{aligned}\)**

**The average air speed in duct is given as:**

**\(v = \frac{V}{{A \cdot t}}\)**

**Substitute all the values in the above equation.**

**\(\begin{aligned}v &= \frac{{\left( {13\;{\rm{m}} \times 20\;{\rm{m}} \times 2.75\;{\rm{m}}} \right)}}{{\left( {0.071\;{{\rm{m}}^2}} \right)\left( {900\;{\rm{s}}} \right)}}\\v &= 10.33\;{\rm{m}}/{\rm{s}}\end{aligned}\)**

**Therefore, the average air speed in duct is \(10.33\;{\rm{m}}/{\rm{s}}\).**

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