Question
Download Solution PDFA compound piping system consists of 1500 m of 50 cm, 600 m of 40 cm and 400 m of 30 cm diameter pipes of the same material connected in series. Calculate the equivalent length of a 40 cm pipe of the same material.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given data:
Length of the first pipe (L1) = 1500 m
Diameter of first pipe (D1) = 50 cm or 0.50 m
Length of the second pipe (L2) = 600 m
Diameter of second pipe (D2) = 40 cm or 0.40 m
Length of the third pipe (L3) = 400 m
Diameter of third pipe (D3) = 30 cm or 0.30 m
Diameter equivalent pipe (D) = 40 cm or 0.4 m
Length of equivalent pipe (L) =?
In series combination length of the equivalent pipe is given by -
\({L\over D^5}={L_{1}\over D_{1}^5}+{L_{2}\over D_{2}^5}+{L_{3}\over D_{3}^5}+...\)
\({L\over 0.4^5}={1500\over 0.5^5}+{600\over 0.4^5}+{400\over 0.3^5}\)
\(L=0.4^5[{1500\over 0.5^5}+{600\over 0.4^5}+{400\over 0.3^5}]\)
\(L=2777.116\, m\)
Hence, the equivalent length of the pipe is 2778 m.
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