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Question

A 15-m-long garden hose has an inner diameter of 2.5 cm. One end is connected to a spigot; 20C20 ^ { \circ } \mathrm { C } water flows from the other end at a rate of 1.2 L/s. What is the gauge pressure at the spigot end of the hose? A. 1900 Pa B. 2700 Pa C. 4200 Pa D. 5800 Pa E. 7300 Pa

Solution

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Poiseuille's equation for viscous fluid flow is

Q=πR4Δp8ηLQ=\dfrac{\pi R^4 \Delta p}{8\eta L}

Given,

Radius R=2.5/2=1.25R=2.5/2=1.25 cm =0.0125=0.0125 m

Viscosity η=1.0×103\eta=1.0\times10^{-3} Pa-s

Length L=15L=15 m

Flow rate Q=1.2Q=1.2 L/s =1.2×103=1.2\times10^{-3} m3/^3/s

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