B.5 Homework 5¶

ChE 316 – Chem Eng. Fluid Mechanics – Spring 2024

DUE 7 Feb 2024

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

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try:
    import pint
except:
    !pip install pint
    import pint
finally:
    ur = pint.UnitRegistry()

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try:
    import CoolProp.CoolProp as CP
except:
    !pip install CoolProp
    import CoolProp.CoolProp as CP

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# 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. The entrance length refers to the distance along a tube needed before the flow profile is fully developed. In laminar flow the entrance length, $x_t$, can be estimated as $x_t=0.05 D (Re)$. However, for turbulent flow, a rule of thumb is often applied such that the entrance length can be estimated as $x_t≈10D$. This is a rough estimate, and a more accurate description of the entrance length can be determined from the equation $x_t=1.36 D(Re)^{1/4}$.

Now, assume a pipe diameter of 20 cm.

Generate a graph of turbulent flow entrance length (in m) versus Reynolds number in the range 1000 to $1\times 10^5$.
At what Reynolds number does the "rule of thumb" become a poor estimate assuming the rule fails to be effective when the estimation error exceeds 5%. In other words, at what Reynolds number does the turbulent description of entrance length exceed the "rule of thumb" by 5%?
Discussion: What additional adjustments can be made to the rule of thumb to increase its accuracy.

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# YOUR SOLUTION HERE

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