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Hydraulic Analoqy -


REF.FIG. B

Consider a short column of fluid of length dr at radius r from axis of rotation of the tube. Them if velocity of fluid relative to tube is V and angular velocity of tube is ꞷ then coriolli’s component of acceleration is 2 V ꞷ in a direction perpendicular to rotation of tube. The torque dT applied by the tube to produce this acceleration is then

dW

dT = ------------- 2 V ꞷ r

Where, dW is weight of short column of fluid.

If W be the specific weight of fluid and a is cross sectional area of tube, then ,

dW = W a dr

W a dr

dT = ----------- 2 V ꞷ r



g

and total torque applied to column of length I ,

I w

T = / 2 ---------- V ꞷ a . r. dr



0 g
W

T = ------------- w V . a I2


g

Hence , coriolli’s component of acceleration,

^^ 2 g T

G A = -------------

W a I2


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