QUESTION 1 Later on in the course, you will learn how to use the Navier-Stokes equations to predict the flow behaviour of Newtonian fluids in various systems with fairly simple geometries. Below is a schematic for the pressure-driven flow of a Newtonian fluid in the annular space between two concentric cylinders - the inner cylinder has radius Ri and the outer cylinder has radius Ro. PO>PL 2R₁ 2R0 Four of your colleagues attempted to solve the Navier-Stokes equations to determine an expression for Q, the volumetric flow rate of fluid, in terms of the following parameters:
QUESTION 1 Later on in the course, you will learn how to use the Navier-Stokes equations to predict the flow behaviour of Newtonian fluids in various systems with fairly simple geometries. Below is a schematic for the pressure-driven flow of a Newtonian fluid in the annular space between two concentric cylinders - the inner cylinder has radius Ri and the outer cylinder has radius Ro. PO>PL 2R₁ 2R0 Four of your colleagues attempted to solve the Navier-Stokes equations to determine an expression for Q, the volumetric flow rate of fluid, in terms of the following parameters:
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![QUESTION 1
Later on in the course, you will learn how to use the Navier-Stokes equations to predict the flow behaviour of
Newtonian fluids in various systems with fairly simple geometries. Below is a schematic for the pressure-driven flow
of a Newtonian fluid in the annular space between two concentric cylinders - the inner cylinder has radius Ri and the
outer cylinder has radius Ro.
PO>PL
• the applied pressure (AP)
Four of your colleagues attempted to solve the Navier-Stokes equations to determine an expression for Q, the
volumetric flow rate of fluid, in terms of the following parameters:
the length of the annular space (Z)
the viscosity of the fluid (μ)
Unfortunately they each came up with a different expression for Q:
Q
TR² AP
πR ΔΡ
-|- -|-
Q
=
8μ L
8μ L
*
Ro
Z
AP
-A1-(-)*
8μ L
Ro
¹ (R₂)
In
2R₁2R0
¹-(₂)]²*
¹ (R₂)
In
Q
TRAP
8μ L
-(.*.
R₁
Ro
[p()]
(R₂)
Ro
In
1- (+)²] ²
(Ro
R₁
In
Using a dimensional analysis, determine which (if any) of the four might be the correct equation for Q.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2F9acdd8d6-4cb4-4e62-b002-4950d6640803%2Fllre0nc_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 1
Later on in the course, you will learn how to use the Navier-Stokes equations to predict the flow behaviour of
Newtonian fluids in various systems with fairly simple geometries. Below is a schematic for the pressure-driven flow
of a Newtonian fluid in the annular space between two concentric cylinders - the inner cylinder has radius Ri and the
outer cylinder has radius Ro.
PO>PL
• the applied pressure (AP)
Four of your colleagues attempted to solve the Navier-Stokes equations to determine an expression for Q, the
volumetric flow rate of fluid, in terms of the following parameters:
the length of the annular space (Z)
the viscosity of the fluid (μ)
Unfortunately they each came up with a different expression for Q:
Q
TR² AP
πR ΔΡ
-|- -|-
Q
=
8μ L
8μ L
*
Ro
Z
AP
-A1-(-)*
8μ L
Ro
¹ (R₂)
In
2R₁2R0
¹-(₂)]²*
¹ (R₂)
In
Q
TRAP
8μ L
-(.*.
R₁
Ro
[p()]
(R₂)
Ro
In
1- (+)²] ²
(Ro
R₁
In
Using a dimensional analysis, determine which (if any) of the four might be the correct equation for Q.
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