2. In class, we discussed several different flow scenarios for which we can make enough assumptions to simplify the Navier-Stokes equations enough to solve them and obtain an exact solution. Consulting the cylindrical form of the Navier-Stokes equations copied below, please answer the following questions. др a 1 a + +0x- + +O₂ = Pgr + μl 18²v, 2 ave ²v₁] az2 + at or r de r Əz dr ar Vodvz др [18 + + +Or + +Vz = Pgz +fl at ar r 20 ôz ôz dr ave дов V,Ve ave +Or + + = pge at dr r 80 Əz + az2 a.) In class, we discussed how the Navier-Stokes equations are an embodiment of Newton's 2nd law, F = ma (where bolded terms are vectors). Name the 3 forces that we are considering in our analysis of fluid flow for this class. др a 10 1 ve 2 av 2200] + +μ or 42 30 b.) If we make the assumption that flow is "fully developed" in the z direction, which term(s) would go to zero? Write the term below, describe what the term means in simple language (i.e. do not simply state "it is the derivative of a with respect to b"). You may (optionally) include a simple sketch/illustration to help clarify your explanation.

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter15: Fluids
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2. In class, we discussed several different flow scenarios for which we can make enough
assumptions to simplify the Navier-Stokes equations enough to solve them and obtain
an exact solution. Consulting the cylindrical form of the Navier-Stokes equations copied
below, please answer the following questions.
др
a
1 a
+
+0x-
+
+O₂
= Pgr
+ μl
18²v, 2 ave ²v₁]
az2
+
at
or
r de r
Əz
dr
ar
Vodvz
др
[18
+
+
+Or
+
+Vz
= Pgz
+fl
at
ar
r 20
ôz
ôz
dr
ave
дов
V,Ve
ave
+Or
+
+
= pge
at
dr r 80
Əz
+
az2
a.) In class, we discussed how the Navier-Stokes equations are an embodiment of Newton's
2nd law, F = ma (where bolded terms are vectors). Name the 3 forces that we are considering in
our analysis of fluid flow for this class.
др a 10
1 ve 2 av 2200]
+
+μ
or
42 30
b.) If we make the assumption that flow is "fully developed" in the z direction, which term(s)
would go to zero? Write the term below, describe what the term means in simple language (i.e.
do not simply state "it is the derivative of a with respect to b"). You may (optionally) include a
simple sketch/illustration to help clarify your explanation.
Transcribed Image Text:2. In class, we discussed several different flow scenarios for which we can make enough assumptions to simplify the Navier-Stokes equations enough to solve them and obtain an exact solution. Consulting the cylindrical form of the Navier-Stokes equations copied below, please answer the following questions. др a 1 a + +0x- + +O₂ = Pgr + μl 18²v, 2 ave ²v₁] az2 + at or r de r Əz dr ar Vodvz др [18 + + +Or + +Vz = Pgz +fl at ar r 20 ôz ôz dr ave дов V,Ve ave +Or + + = pge at dr r 80 Əz + az2 a.) In class, we discussed how the Navier-Stokes equations are an embodiment of Newton's 2nd law, F = ma (where bolded terms are vectors). Name the 3 forces that we are considering in our analysis of fluid flow for this class. др a 10 1 ve 2 av 2200] + +μ or 42 30 b.) If we make the assumption that flow is "fully developed" in the z direction, which term(s) would go to zero? Write the term below, describe what the term means in simple language (i.e. do not simply state "it is the derivative of a with respect to b"). You may (optionally) include a simple sketch/illustration to help clarify your explanation.
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