Question

A pipe is horizontal and carries oil that has a viscosity of 0.14 Pa s. The volume flow rate of the oil is 5.3 × 10-5 m3/s. The length of the pipe is 37 m, and its radius is 0.58 cm. At the output end of the pipe the pressure is atmospheric pressure. What is the absolute pressure at the input end?

Answer 1

Answer:

Explanation:

Given

$\mu =0.14 Pa.s$

Volume Flow rate $Q=5.3\times 10^{-5} m^3/s$

Length $L=37 m$

radius $r=0.58 cm$

$D=1.16 cm$

According to Hagen-Poiseuille Equation

difference in Pressure is given

$\Delta P=\frac{128\mu L\cdot Q}{\pi D^4}$

$P_{in}-P_{out}=\frac{128\mu L\cdot Q}{\pi D^4}$

$P_{in}=P_{out}+\frac{128\mu L\cdot Q}{\pi D^4}$

$P_{in}=1.01325\times 10^5+\frac{128\times 0.14\times 37\times 5.3\times 10^{-5}}{\pi\cdot 1.16^4\times 10^{-8}}$

$P_{in}=1.01325\times 10^5+6.17\times 10^5$

$P_{in}=7.19\times 10^5$