Chapter 4 DIMENSIONAL ANALYSIS AND DYNAMIC SIMILITUDE.
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F = ma (4.2.1)
F = MLT-2 (4.2.2)
which shows that only three of the dimensions are independent. F is the force dimension, M the mass dimension, L the length dimension, and T the time dimension.
- the exponents are to be determined each Π is dimensionless. The dimensions of the A quantities are substituted, and the exponents of M, L, and T are set equal to zero respectively. These produce three equations in three unknowns for each Π parameter, so that the x, y, z exponents can be determined, and hence the Π parameter.
or solve for one of the Π's explicitly:
- are of importance in correlating experimental data.
in which l may refer to orifice diameter and l1 and l2 to upstream dimensions.
Viscosity and surface tension are unimportant for large orifices and low-viscosity fluids. Mach number effects may be very important for gas flow with large pressure drops, i.e., Mach numbers approaching unity.
since surface tension and compressible effects are usually unimportant.
Figure 4.2 Wind tunnel tests on an aircraft carrier superstructure. Model is inverted and suspended from ceiling.
Model tests showing the influence of a bulbous bow on bow wave