Question 1 of 3 · Dimensional Analysis and Similarity · Intermediate · About 21 min
Determine an experimental force-law scale
An experiment uses a compact submerged probe whose measured drag is represented by . Here is force, density, stream speed, a characteristic length, and is dimensionless. Determine exponents by dimensional consistency. Then estimate force for , , and . Use the specific empirical law stated rather than a conventional coefficient area convention.
Given
F=C rho^a U^b D^c
C=0.75 dimensionless
Density: 1030 kg/m³
Speed: 1.80 m/s
Length scale: 0.160 m
Find
Exponents a, b, c
Force from the stated law
Assumptions
C is dimensionless.
No other independent physical variables enter this empirical relation.
Worked solution
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