This question is incomplete, the complete question is;
(Laminar flow) A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of length 2[tex]l[/tex]. The flow is laminar and fully developed. The pressure drop for the first pipe is 1.657 times greater than it is for the second pipe. If the diameter of the first pipe is D, determine the diameter of the second pipe.
Dā = _____D.
{ the tolerance is +/-3% }
Answer:
the diameter of the second pipe Dā is 1.13D
Explanation:
Given the data in the question;
Length = 2[tex]l[/tex]
pressure drop in the first pipe is 1.657 times greater than it is for the second pipe.
Now, we know that for Laminar Flow;
V' = ĻDā“ĪP / 128Ī¼L
where V'ā = V'ā and ĪPāāā = 1.657 ĪPāāā
Hence,
V'ā = ĻDā“ĪPāāā / 128Ī¼L Ā = V'ā = ĻDāā“ĪPāāā / 128Ī¼L
so
Dā = D[tex]([/tex] ĪPāāā / ĪPāāā [tex])^{\frac{1}{4}[/tex]
we substitute
Dā = D[tex]([/tex] 1.657 [tex])^{\frac{1}{4}[/tex]
Dā = D( 1.134568 )
Dā = 1.13D
Therefore, the diameter of the second pipe Dā is 1.13D
