This notebook contains material from chemeng316_fluids; content is available on Github.

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B.6 Homework 6¶

ChE 316 – Chem Eng. Fluid Mechanics – Spring 2024

DUE 9 Feb 2024

Getting Started: Here is the code to import the pint, CoolProp, numpy, sympy, and matplotlib modules to get you started.

In [ ]:
try:
    import pint
except:
    !pip install pint
    import pint
finally:
    ur = pint.UnitRegistry()
In [ ]:
try:
    import CoolProp.CoolProp as CP
except:
    !pip install CoolProp
    import CoolProp.CoolProp as CP
In [ ]:
# we need numpy for constants like pi
# https://numpy.org/doc/stable/reference/constants.html
import numpy as np

# we often use sympy to solve equations
import sympy as sp

# for plotting we need
import matplotlib.pyplot as plt

# For nice plotting I include ...
plt.rcParams['mathtext.default'] = 'rm'
plt.rcParams['mathtext.fontset'] = 'stix'
plt.rcParams['font.family'] = 'Times New Roman'

Problem 1. Fluid is trapped between two parallel vertical plate that are separated by a distance $L=1$ mm. The plate located at $x=L$ moves vertically with constant velocity $V_0$ (see example 4.3 in the textbook). The fluid is an oil with a density of $\rho=900$ kg/m$^3$ and a viscosity of $\mu=50$ mPa$\cdot$s. The pressure drop, $dP/dy$, is negligible compared with the gravity term, $\rho g$.

  • (a) What is the minimum upward velocity, $V_{0,min}$, of the moving plate so that all the fluid moves upward?
  • (b) Plot the velocity, $v(x)$ for $V_0 = V_{0,min} \pm $10%. This should be three curves, one for each value of $V_0$.
  • (c) What is the velocity midway between the plates when $V_0$ is set at the minumum value from Part (a).
  • (d) What is the shear rate, $\tau$ in the fluid at $x=0$, $x=L/2$, and $x=L$.
In [ ]:
# YOUR SOLUTION HERE

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