Answer to Question #184380 in Mechanics | Relativity for Konoha

Question

The main uptake air duct of a forced air gas heater is 0.4 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 13 min? The inside volume of the house is equivalent to a rectangular solid 10.29 m wide by 11.11 m long by 2.8 m high.

Round your answer to 2 decimal places

Answer 1

Volumetric flow rate$(Q)$, is given as,

$Q=Av$

$A:$ Area of cross section of duct

$v:$ velocity of flow

Also,

$Q=\dfrac{V}{t}$

$Av=\dfrac{V}{t}$

$v=\dfrac{V}{At}=\dfrac{LBH}{\dfrac{\pi d^2}{4}t}$

$v=\dfrac{10.29\times11.11\times2.8}{\dfrac{\pi\times(0.4)^2}{4}\times(13\times60)}$

$v=3.26\space m/s$