A U-tube manometer, as shown in Fig.17.11, contains a fluid of density ρ. Calculate the frequency of free oscillations of the fluid.
Question 17.3: A U-tube manometer, as shown in Fig.17.11, contains a fluid ...
Let l = length of U-tube containing the fluid
A = area of cross-section of the tube
Fluid mass, m = ρ Al
x = displacement of fluid column
Weight of fluid responsible for restoring the original fluid level,
W=2 \rho \operatorname{Ag} x .
The equation of motion becomes,
m \ddot{x}+W=0 .
\rho A l \ddot{x}=2 \rho A g x=0 .
\ddot{x}+\frac{2 g}{l} x=0 .
\omega_{n}=\sqrt{\frac{2 g}{l}} rad / s .
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