Pressure Variation –
Rigid Body Motion
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Example: The
U-tube shown below is partially filled with a liquid. This device undergoes a constant,
horizontal acceleration,
a , to the right. A
differential reading, h, develops between The
legs of the manometer which are spaced a distance, L, apart. Find the relationship between a, L, and h. Strategy: Apply the equation of motion for constant
acceleration in the x-direction. -
∂P/∂x = ρax =
ρa Apply the
equation of motion in the z-direction.
- ∂P/∂z =
γ = ρ g Now P = P(x,z). So dP
= (∂P/∂x) dx + (∂P/∂z)dz = -
ρa dx -
ρ g dz But
on the free surface dP =
0 = - ρa (L) - ρg (-h) So h
= L(a/g) (result) Click
here for another example. |
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