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A gate with mass m and length 2L is suspended at one end by a hinge at the free surface of a...

Question:

A gate with mass m and length 2L is suspended at one end by a hinge at the free surface of a reservoir. The bottom of the gate is free to move. The gate is at an angle {eq}\theta {/eq} with respect to the vertical. The reservoir contains two layers of different liquids:

- the upper liquid layer of depth L has specific weight of {eq}\gamma {/eq}

-the lower liquid later, also of depth L, has a specific weight {eq}C_\gamma {/eq}, where C is a constant (C > 1).

Assume that everything has a unit dimension normal to the page.

Derive an expression fro the gage pressure distrubution {eq}p_1(z) {/eq} in the top fluid (i.e., {eq}0<z\leq L {/eq}) and {eq}p_2(z) {/eq} in the bottom fluid (i.e., {eq}L\leq z \leq 2L {/eq}.

Static Pressure

A fluid resting in a gravitational field exerts on all bodies immersed in it, according to the Pascal principle, an all-round static pressure which, according to Pascal's law, increases with depth. Examples of a static pressure are the water pressure and the air pressure.

Answer and Explanation:

For {eq}0<z\leq L {/eq} we have the top fluid which has the specific weight of {eq}\gamma {/eq}.

Also we get the following gage pressure...

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What is Static Pressure? - Definition & Formula

from Introduction to Engineering

Chapter 5 / Lesson 3
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