A commonly used rule of thumb is that the average velocity in pipe should be about 1m/s or less"thin" fluids( viscosity about water). if pipe needs to deliver 6000m of water per day, what diameter is required to satisfy the 1-m/s rule?
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To determine the diameter of the pipe required to satisfy the 1 m/s velocity rule, we need to use the equation for flow rate:
Flow rate (Q) = Velocity (V) x Cross-sectional Area (A)
In this case, we want to deliver 6000 m^3 (cubic meters) of water per day. Since we know the desired velocity (V) is 1 m/s, we can rearrange the equation to solve for cross-sectional area (A):
A = Q / V
Let's calculate the value for cross-sectional area (A) based on the given flow rate:
Q = 6000 m^3/day
V = 1 m/s
Plugging these values into the equation, we get:
A = 6000 m^3/day / 1 m/s = 6000 m^2/day
However, the units of m^2/day are not convenient for pipe diameter calculations. We need to convert it to a more appropriate unit, such as square meters per second (m^2/s). Since there are 24 hours in a day and 60 seconds in a minute, we can convert the units as follows:
1 m^2/day = (1 m^2/24 hours) x (1 hour/60 minutes) x (1 minute/60 seconds) = 0.0000116 m^2/s
Now, we can calculate the required cross-sectional area in square meters per second:
A = 6000 m^2/day x 0.0000116 m^2/s = 0.0696 m^2/s
Since we are dealing with a circular pipe, we can use the formula for the cross-sectional area of a circle to find the diameter (d):
A = π * (d/2)^2
Rearranging the equation to solve for d:
d = √(4A/π)
Plugging in the value for cross-sectional area (A), we get:
d = √(4 x 0.0696 m^2/s / π) = √(0.0882 / π) = √0.0281 = 0.1677 m
The diameter of the pipe required to satisfy the 1 m/s velocity rule is approximately 0.1677 meters or 167.7 millimeters.