handbook of modern sensors

378 Flow Sensors
The drag force F , exerted by incompressible fluid on a solid object exposed to it
is given by the drag equation:
F D = C D ρAV 2 , (11.28)
where ρ is the fluid density, V is the fluid velocity at the point of measurement,
A is the projected area of the body normal to the flow, and C D is the overall drag
coefficient. C D is a dimensionless factor whose magnitude depends primarily on the
physical shape of the object and its orientation relative to the fluid stream. If mass of
the supporting beam is ignored, the developed strain is
ε = 3C DρAV 2 (L − x)
Ea 2 , (11.29)
b
where L is the beam length, x is the point coordinate on the beam where the strain
gauges are located, E is Young’s modulus of elasticity, and a and b are the geometry
target factors. It is seen that the strain in a beam is a square-law function of the fluid
speed.
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