
Concept explainers
Figure 12.7 shows a branched system in which the pressure at A is

Total volume flow rate by using the given information.
Answer to Problem 12.1PP
The total volume flow rate is determined below.
Explanation of Solution
First we have to find the head loss at point A and B on applying the energy equation.
Here
And then parallel system head losses for both the parts are same
Then substitute
Then the roughness of steel pipe is
Inside diameter of the pipe is
Find the relative roughness of the elbow
Corresponding to friction factor value is
Find the total head loss of the upper section
For 900 elbows curved, effective length ratio is
Substitute required values we will get
From the table of text book DN 80 pipes the inside diameter of the pipe is 0.0779m
Find the relative rough ness
Find the total head loss of the lower branch we will get
Substitute above values we get
Assume
Find the flow velocity at upper branch
Substitute above value we get
Find the Reynolds number for the flow
Find the relative roughness we get
Then the value of friction factor is
Find the flow velocity at B
Substitute above values we get
Calculate the Reynolds number for the flow
Substitute above values we get
Find the relative roughness value
Then the value of friction factor is
Recomputed the velocity of flow using above equation
Find the Reynolds number for the flow
Substitute above values we get
Find the value of relative roughness
From Moody's diagram, the value of relative roughness and Reynolds number
Find the flow rate at A,
We get
Find the flow rate at B
Total volume flow rate is
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