At low velocities (laminar flow), the volume flow Q through a small-bore tube is a function only of the tube radius R, the fluid viscosity ?܇, and the pressure drop per unit tube length dp/dx. Using the Buckingham pi theorem, find an appropriate dimensionless relationship. Make use of Table 1 Table 1: Dimensional AnalysisQuantityAreaVolumeVelocityAccelerationAngular velocityForceMassDensitySpecific weightPressureDynamic viscosityKinematic viscosityPowerVolumetric flow rateMass flow rateSurface tensionWeightTorqueSymbolAVVa@FmPYPμVWQmσWTM-L-TL²L³LT-1LT-2T-1MLT-2MML-3ML-²T-2ML-¹T-2ML-¹T-¹L²T-1ML²T-3L³T-1MT-1MT-2MLT-2ML²T-²F-L-TL²L³LT-1LT-2T-1FFT²L-¹FT²L-4FL-3FL-2FTL-2L²T-1FLT-1L³T-1FTL-¹FL-1FFL

Given: As stated in the question description, we can express the volume flow rate Q as,…

Answered: At low velocities (laminar flow), the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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At low velocities (laminar flow), the volume flow Q through a small-bore tube is a function only of the tube radius R, the fluid viscosity ?܇, and the pressure drop per unit tube length dp/dx. Using the Buckingham pi theorem, find an appropriate dimensionless relationship. Make use of Table 1

Table 1: Dimensional Analysis
Quantity
Area
Volume
Velocity
Acceleration
Angular velocity
Force
Mass
Density
Specific weight
Pressure
Dynamic viscosity
Kinematic viscosity
Power
Volumetric flow rate
Mass flow rate
Surface tension
Weight
Torque
Symbol
A
V
V
a
@
F
m
P
Y
P
μ
V
W
Q
m
σ
W
T
M-L-T
L²
L³
LT-1
LT-2
T-1
MLT-2
M
ML-3
ML-²T-2
ML-¹T-2
ML-¹T-¹
L²T-1
ML²T-3
L³T-1
MT-1
MT-2
MLT-2
ML²T-²
F-L-T
L²
L³
LT-1
LT-2
T-1
F
FT²L-¹
FT²L-4
FL-3
FL-2
FTL-2
L²T-1
FLT-1
L³T-1
FTL-¹
FL-1
F
FL

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