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(a) (Room volume)/(840 s) = ______ m^3/s
(b) (Flow rate)/(duct area)
A room measures 4.0 m by 3.9 m by 4.5 m. The heating and air-conditioning ducts to and from the room are circular with diameter 0.37 m and all the air in the room is to be exchanged every 14 min.
(a) What is the average flow rate?
m3/s
(b) What is the necessary flow speed in the duct? (Assume that the density of the air is constant.)
drwls
answered12 years ago
Explain Bot
answered11 months ago
To find the average flow rate and the necessary flow speed in the duct, we can use the formula for flow rate:
Flow Rate = Volume / Time
Let's break down the problem step by step:
Step 1: Find the volume of the room.
The volume of the room can be found by multiplying the length, width, and height together.
Volume = length x width x height
Volume = 4.0 m x 3.9 m x 4.5 m
Step 2: Convert the time from minutes to seconds.
Since flow rate is typically measured in cubic meters per second (m^3/s), we need to convert the time from minutes to seconds.
1 min = 60 s
Therefore, the time in seconds is 14 min x 60 s/min.
Step 3: Calculate the average flow rate.
To find the average flow rate, divide the volume of the room by the time in seconds.
Average Flow Rate = Volume / Time
Step 4: Find the cross-sectional area of the duct.
The cross-sectional area of the duct can be found using the formula for the area of a circle.
Area = π * (radius)^2
Since we are given the diameter of the duct (0.37 m), we need to divide it by 2 to get the radius.
Step 5: Calculate the necessary flow speed in the duct.
To find the flow speed, divide the average flow rate by the cross-sectional area of the duct.
Flow Speed = Average Flow Rate / Cross-sectional Area
Let's plug in the values and calculate the answers.
(a) Average flow rate:
Volume = 4.0 m x 3.9 m x 4.5 m
Time = 14 min x 60 s/min
Average Flow Rate = Volume / Time
(b) Necessary flow speed in the duct:
Cross-sectional Area = π * (radius)^2
Flow Speed = Average Flow Rate / Cross-sectional Area