R₂ = 20 mmFlow-Liquidp= 1000 kg/m³μ = 0.02 Pa sRi. ARoA liquid flows through the space between a small rod and a pipe, as shown in diagram below.The outer radius of the pipe is R₁, the inner radius of the rod is R₁, and the ratio λpressure difference per unit length (Ap/L) of 2000 Pa/m is applied to drive the fluid flow. Theliquid has a viscosity of μ = 0.02 Pa's.Q = πIf the equation of volumetric flow rate (Q) of the liquid, is given asApR" ApR" (Ri8μ L 8μ L+-20%4RR₁ = AR₁ = 10 mm+RoRi(A) What should be the value of "n", for the equation above to be dimensionally consistent? Usedimensional analysis.n(1-2²)² ApR"8μ LIn==.(B) Calculate the value of volumetric flow rate in cubic meter per second when r = (Ro+R₁)/2, and Ro = 20mm, R₁ = 10mm. Report your result with three significant figures.

Dimensions of (Q) Q=m3s Dimension of Q must equal to each term on the right hand side : Taking the…

R₁ = 20 mm Flow μ = 0.02 Pa s RAR, 10 mm liquid flows through the space between a small rod and a pipe, as shown in diagram below. Ri he outer radius of the pipe is Ro, the inner radius of the rod is R₁, and the ratio = A Ro ressure difference per unit length (Ap/L) of 2000 Pa/m is applied to drive the fluid flow. The quid has a viscosity of μ = 0.02 Pa's. the equation of volumetric flow rate (Q) of the liquid, is given as

R₁ = 20 mm Flow μ = 0.02 Pa s RAR, 10 mm liquid flows through the space between a small rod and a pipe, as shown in diagram below. Ri he outer radius of the pipe is Ro, the inner radius of the rod is R₁, and the ratio = A Ro ressure difference per unit length (Ap/L) of 2000 Pa/m is applied to drive the fluid flow. The quid has a viscosity of μ = 0.02 Pa's. the equation of volumetric flow rate (Q) of the liquid, is given as

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

R₂ = 20 mm
Flow-
Liquid
p= 1000 kg/m³
μ = 0.02 Pa s
Ri. A
Ro
A liquid flows through the space between a small rod and a pipe, as shown in diagram below.
The outer radius of the pipe is R₁, the inner radius of the rod is R₁, and the ratio λ
pressure difference per unit length (Ap/L) of 2000 Pa/m is applied to drive the fluid flow. The
liquid has a viscosity of μ = 0.02 Pa's.
Q = π
If the equation of volumetric flow rate (Q) of the liquid, is given as
ApR" ApR" (Ri
8μ L 8μ L
+
-20%
4
R
R₁ = AR₁ = 10 mm
+
Ro
Ri
(A) What should be the value of "n", for the equation above to be dimensionally consistent? Use
dimensional analysis.
n
(1-2²)² ApR"
8μ L
In
==.
(B) Calculate the value of volumetric flow rate in cubic meter per second when r = (Ro+
R₁)/2, and Ro = 20mm, R₁ = 10mm. Report your result with three significant figures.

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