Problem 1

Please calculate the pressure drop through a pipe if its length is \(1 \; km\); its diameter is \(1 m\), and if the fluid has viscosity of \(\require{color}{\color[rgb]{0.501963,0.000046,0.501966}\mu} = {\color[rgb]{0.501963,0.000046,0.501966}1.54 \; 10^{-3} kg/(m \cdot s)}\) and the bulk velocity is \(\require{color}{\color[rgb]{0.059472,0.501943,0.998465}10\; m/s}\).

This is a straightforward application of the Hagen-Poiseuille equation for the pressure loss across a pipe. Recall, from Lecture 10 we found out that

\[ \large \require{color}\Delta {\color[rgb]{0.315209,0.728565,0.037706}p} = \frac{8 {\color[rgb]{0.501963,0.000046,0.501966}\mu} {\color[rgb]{0.059472,0.501943,0.998465}V} L}{{\color[rgb]{0.990448,0.502245,0.032881}R}^2}. \]

Below we plug in the values to work this out.

Code 
import numpy as np

mu = 1.54 * 10**(-3) # viscosity
V = 10 # velocity
D = 1 # diameter
R = D/2 # radius
L = 1000 # 1 km = 1000 m
Delta_p = (8 * mu * V * L)/(R**2)
print('The loss in pressure is '+str(np.around(Delta_p,3))+'Pa')
The loss in pressure is 492.8Pa