Fluids and Oscillations

Can anyone prove the oscillation of a fluid in a U-tube or a bent V tube is a SHM for small displacements using Bernoulli's theorem?

Help!!

#Mechanics

Easy Math Editor

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Comments

If you recall, Bernoulli's equation assumes steady state fluid flow. Since the fluid oscillating in the U-tube is changing direction, there's no steady flow. There's also damping and turbulence. Long story short, Bernoulli's equation does not apply here.

Josh Silverman Staff - 4 years, 6 months ago

If we assume there is no damping can we apply it then?

Abhi Kumbale - 4 years, 6 months ago

As long as the flow isn't steady Bernoulli's equation isn't valid.

Josh Silverman Staff - 4 years, 6 months ago

@Josh Silverman – Got it. Thanks.

Abhi Kumbale - 4 years, 6 months ago

@Abhi Kumbale – I remembered this video. Walter Lewin does a demo with the liquid as well as the calculation. (timestamp starts at the demo, calculation is a little bit before.

https://youtu.be/-6vl8HWo3tY?t=1865

Josh Silverman Staff - 4 years, 6 months ago

@Josh Silverman @Aniket Sanghi @Deepanshu Gupta @Nishant Rai @Rohith M.Athreya @Swapnil Das

Abhi Kumbale - 4 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$