Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2019
Medium
Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is the same, the ratio of volume flow rates QB/QA is ___ (round off to two decimal places).
0.5(± 0.02 accepted)
Explanation
For laminar flow, the Hagen-Poiseuille equation gives ΔP ∝ LQ/D⁴ for a fixed diameter. Equal head loss (same ΔP, same D) means LA·QA=LB·QB, so QB/QA=LA/LB=1.0/2.0=0.5.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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