Q/ Consider the film flow of a power-law fluid with parameters к and n and density p down a plate inclined at angle with respect to the horizontal. If the film thickness is H: a. Derive an expression for the resulting velocity profile x as a function of y (distance from the plate), H, к, n, g, p, and 0 b. Sketch three representative velocity profiles (each having, for simplicity, the same maximum velocity, which in practice would mean different values of x), for n < 1, n = 1, and n > 1, and comment briefly on the important features. Power law fluid model is given as: T, = m(-dvx)" where m=k Continuity Equation, Cartesian coordinates dr др at Uz др ǝx др +P + บบ บ ax J+ ลง← + อ! მაქ = Iz Continuity Equation, cylindrical coordinates др 1 (prvr) 1 + at (pv) + + ǝr T a0 ǝ(pv) Dz = 0 Continuity Equation, spherical coordinates др at 1 (pr²vr) 1 + + -2 Ər r sin 0 (pvo sin 0) a0 1 2 (ρυς) + = 0 r sin 0 მი ☐

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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Q/ Consider the film flow of a power-law fluid with parameters к and n
and density p down a plate inclined at angle with respect to the
horizontal. If the film thickness is H:
a. Derive an expression for the resulting velocity profile x as a function of y
(distance from the plate), H, к, n, g, p, and 0
b. Sketch three representative velocity profiles (each having, for simplicity, the
same maximum velocity, which in practice would mean different values of x),
for n < 1, n = 1, and n > 1, and comment briefly on the important features.
Power law fluid model is given as: T, = m(-dvx)" where m=k
Continuity Equation, Cartesian coordinates
dr
др
at
Uz
др
ǝx
др
+P
+ บบ บ
ax
J+
ลง← + อ!
მაქ
=
Iz
Continuity Equation, cylindrical coordinates
др 1 (prvr) 1
+
at
(pv)
+
+
ǝr
T
a0
ǝ(pv)
Dz
= 0
Continuity Equation, spherical coordinates
др
at
1 (pr²vr)
1
+
+
-2
Ər
r sin 0
(pvo sin 0)
a0
1
2 (ρυς)
+
= 0
r sin 0
მი
☐
Transcribed Image Text:Q/ Consider the film flow of a power-law fluid with parameters к and n and density p down a plate inclined at angle with respect to the horizontal. If the film thickness is H: a. Derive an expression for the resulting velocity profile x as a function of y (distance from the plate), H, к, n, g, p, and 0 b. Sketch three representative velocity profiles (each having, for simplicity, the same maximum velocity, which in practice would mean different values of x), for n < 1, n = 1, and n > 1, and comment briefly on the important features. Power law fluid model is given as: T, = m(-dvx)" where m=k Continuity Equation, Cartesian coordinates dr др at Uz др ǝx др +P + บบ บ ax J+ ลง← + อ! მაქ = Iz Continuity Equation, cylindrical coordinates др 1 (prvr) 1 + at (pv) + + ǝr T a0 ǝ(pv) Dz = 0 Continuity Equation, spherical coordinates др at 1 (pr²vr) 1 + + -2 Ər r sin 0 (pvo sin 0) a0 1 2 (ρυς) + = 0 r sin 0 მი ☐
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