The instruction manual for a hot-wire anemometer states that ‘roughly speaking, the current varies as the one-fourth power of the average velocity at a fixed wire resistance’. Check this statement, using the heat transfer characteristics of thin wire in air and water.
GIVEN
• A thin current carrying wire in an air or water stream
FIND
• Show that the current (I) varies as the one-fourth power of the fluid velocity (V?) at a fixed resistance (ReI) ASSUMPTIONS
• Radiative heat transfer is negligible
This solution follows the same procedure as the solution to Problem 6.17
Holding the wire resistance constant has the effect of holding the wire temperature (Ts) and therefore,
the fluid properties constant. Ts, Tb, At, and ReI are constant.
According to
for 40 < Re < 1000 m = 0.5 ? I a U?1/4 Since the wire diameter is typically a few microns, we expect the Reynolds number to be very low. Therefore, m = 0.4 to 0.5 and m/2 = 0.2 to 0.25
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