A sewer of 500 mm diameter installed on slope of 0.40 % and running ¾ full at max Flow if the waste water flow is 200 (L/c/d) with a peak factor of 3 the full flow is.......a.1.0 m3/dayb.0.21 m3/secc.0.25 m3/dayd.0.25 m3/sec
Question
A sewer of 500 mm diameter installed on slope of 0.40 % and running ¾ full at max Flow if the waste water flow is 200 (L/c/d) with a peak factor of 3 the full flow is.......a.1.0 m3/dayb.0.21 m3/secc.0.25 m3/dayd.0.25 m3/sec
Solution
To solve this problem, we need to use the formula for the flow rate in a pipe, which is Q = A * V, where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the flow.
Step 1: Calculate the cross-sectional area of the pipe The pipe is running ¾ full, so we need to calculate the area of the pipe when it is ¾ full. The cross-sectional area of a full pipe is given by the formula A = π * (D/2)^2, where D is the diameter of the pipe.
A = π * (0.5 m / 2)^2 = 0.196 m^2
Since the pipe is running ¾ full, the effective cross-sectional area is 0.75 * 0.196 m^2 = 0.147 m^2.
Step 2: Calculate the velocity of the flow The velocity of the flow can be calculated using the formula V = S * R^(2/3) / n, where S is the slope of the pipe, R is the hydraulic radius, and n is the Manning's roughness coefficient.
Assuming a typical value for n of 0.013 for sewer pipes, and given that the slope S is 0.004 (0.40 %), and the hydraulic radius R is D/4 for a pipe running half full, we get:
V = 0.004 * (0.5 m / 4)^(2/3) / 0.013 = 0.46 m/s
Step 3: Calculate the flow rate Now we can calculate the flow rate Q = A * V:
Q = 0.147 m^2 * 0.46 m/s = 0.067 m^3/s
However, the problem states that the flow rate given is the peak flow rate, which is 3 times the average flow rate. Therefore, the average flow rate is Q / 3 = 0.067 m^3/s / 3 = 0.022 m^3/s.
Step 4: Convert the flow rate to m^3/day To convert the flow rate from m^3/s to m^3/day, we multiply by the number of seconds in a day (86400 s):
Q = 0.022 m^3/s * 86400 s/day = 1900.8 m^3/day
So, the full flow is not listed in the options provided. There might be a mistake in the question or the options provided.
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