Inlet + P1 ང་ Wall P2 Exit Axis of symmetry (b). Simplify the momentum balance equation in the z-direction and show that 1 d μ r r dr dr = dP ལྕ|ལུ dz dP Assuming that P-P -, solve the above equation with appropriate boundary dz L conditions and show that v₁ = P₁˜³₁₂ (a² = r²). 4μL πατ (R-P) (d) Show that the volumetric flow rate Q 8μL
Inlet + P1 ང་ Wall P2 Exit Axis of symmetry (b). Simplify the momentum balance equation in the z-direction and show that 1 d μ r r dr dr = dP ལྕ|ལུ dz dP Assuming that P-P -, solve the above equation with appropriate boundary dz L conditions and show that v₁ = P₁˜³₁₂ (a² = r²). 4μL πατ (R-P) (d) Show that the volumetric flow rate Q 8μL
Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Chapter26: Applications Of Refrigeration Systems
Section: Chapter Questions
Problem 16RQ: A(n)_______varies the frequency of an electronically altered sine wave, which affects the speed of...
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Question
A fluid of density ρ and viscosity μ flows from left to right through the horizontal pipe of radius a and length
L, shown in the figure below. The pressures at the centers of the inlet and exit are P1 and P2 ,
respectively. You may assume that the only non-zero velocity component is vz and that it is not a
function of the angular coordinate, θ.
(a) Simplify the continuity equation and show that vz = vz(r), i.e., it is a function of r only.
(b) Simplify the momentum balance equation in the z-direction and show that it equals equation a in the image
L, shown in the figure below. The pressures at the centers of the inlet and exit are P1 and P2 ,
respectively. You may assume that the only non-zero velocity component is vz and that it is not a
function of the angular coordinate, θ.
(a) Simplify the continuity equation and show that vz = vz(r), i.e., it is a function of r only.
(b) Simplify the momentum balance equation in the z-direction and show that it equals equation a in the image
(c) Assuming that (dP/dz)=-delta P/L , solve the above equation with appropriate boundary
conditions and show that it equals equation c in the image
(d) Show that the volumetric flow rate equals equation d in the image
conditions and show that it equals equation c in the image
(d) Show that the volumetric flow rate equals equation d in the image
Transcribed Image Text:Inlet
+
P1
ང་
Wall
P2
Exit
Axis of
symmetry
Transcribed Image Text:(b).
Simplify the momentum balance equation in the z-direction and show that
1 d
μ
r
r dr
dr
=
dP
ལྕ|ལུ
dz
dP
Assuming that
P-P
-, solve the above equation with appropriate boundary
dz
L
conditions and show that
v₁ = P₁˜³₁₂ (a² = r²).
4μL
πατ (R-P)
(d)
Show that the volumetric flow rate Q
8μL
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