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# A 15-m-long garden hose has an inner diameter of 2.5 cm. One end is connected to a spigot; $20 ^ { \circ } \mathrm { C }$ 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

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

Given,

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

Viscosity $\eta=1.0\times10^{-3}$ Pa-s

Length $L=15$ m

Flow rate $Q=1.2$ L/s $=1.2\times10^{-3}$ m$^3/$s

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