Question:
Two reservoirs at different levels are connected by two parallel pipes of diameter \(2d\) and \(d\). The ratio of the flows in the larger to smaller pipe is
Two reservoirs at different levels are connected by two parallel pipes of diameter \(2d\) and \(d\). The ratio of the flows in the larger to smaller pipe is
Show Hint
For parallel pipes having equal head loss,
\[
\boxed{
Q\propto D^{5/2}
}
\]
Thus,
\[
\boxed{
\frac{Q_1}{Q_2}
=
\left(\frac{D_1}{D_2}\right)^{5/2}.
}
\]
Updated On: Jul 23, 2026
- \(\sqrt{2}:1\)
- \(2:1\)
- \(4:1\)
- \(4\sqrt{2}:1\)
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The Correct Option is D
Solution and Explanation
Concept:
For two parallel pipes connecting the same reservoirs,
the head loss in each pipe is the same.
Using Darcy-Weisbach equation,
\[
h_f\propto\frac{Q^2}{D^5}
\]
Since the head losses are equal,
\[
\frac{Q_1^2}{D_1^5}
=
\frac{Q_2^2}{D_2^5}.
\]
Therefore,
\[
\boxed{
\frac{Q_1}{Q_2}
=
\left(\frac{D_1}{D_2}\right)^{5/2}
}
\]
Step 1: Write the given diameters. \[ D_1=2d, \] \[ D_2=d. \]
Step 2: Calculate the discharge ratio. \[ \frac{Q_1}{Q_2} = \left(\frac{2d}{d}\right)^{5/2} = 2^{5/2} = 4\sqrt2. \] Hence, \[ \boxed{ Q_1:Q_2 = 4\sqrt2:1. } \] Therefore, the correct option is \[ \boxed{(D)\;4\sqrt2:1.} \]
Step 1: Write the given diameters. \[ D_1=2d, \] \[ D_2=d. \]
Step 2: Calculate the discharge ratio. \[ \frac{Q_1}{Q_2} = \left(\frac{2d}{d}\right)^{5/2} = 2^{5/2} = 4\sqrt2. \] Hence, \[ \boxed{ Q_1:Q_2 = 4\sqrt2:1. } \] Therefore, the correct option is \[ \boxed{(D)\;4\sqrt2:1.} \]
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