Okay, so first things first, pressure is pretty much a measure of how much force is being applied over a certain area. Imagine lying down and having a fluffy kitten walk on you – cute and comfy, right? But if that same kitten wore stiletto heels (ouch!), the pressure those tiny heels would exert would be far greater because the force (kitten’s weight) is being spread over a teeny-tiny area. This is where our first formula comes in:

\[ P = \frac{F}{A} \]

Where:

\( P \) is the pressure

\( F \) is the force

\( A \) is the area

Now, when we’re talking about fluids, things get a tad more interesting. Imagine you’re diving in a pool. The deeper you go, the more water is above you. This means more weight and thus, more pressure. The pressure due to a column of fluid is given by:

\[ P = \rho g h \]

Where:

\( P \) is the pressure

\( \rho \) (rho) is the fluid’s density

\( g \) is the acceleration due to gravity (thanks Earth!)

\( h \) is the height of the fluid column above the point in question

So, you might be wondering, when do you use which formula? Easy peasy:

– If a question starts chatting about forces and areas (maybe a shoe pressing on something or a piston in a cylinder), go for \( P = \frac{F}{A} \).

– On the other hand, if there’s mention of fluid columns, depths, or anything “height” related (like diving in a pool or oil in a barrel), it’s all about \( P = \rho g h \).

Pro tip: If you’re given a change in height and asked about the change in pressure, don’t get bogged down with the whole equation! Pressure changes proportionally with height. Double the height? Double the pressure. Halve the height? You got it, halve the pressure!

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In a hydraulic press, a force of 150 N is applied to a small piston with an area of 0.015 m². What is the pressure being applied to the fluid in the hydraulic system?

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Question 2 of 4

2. Question

At a depth of 5 meters in seawater, the pressure due to the water column is found to be 50 kPa. What would be the pressure at the same depth in a column of mercury with approximately 13.6 times the density of seawater?

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3. Question

If the density of a fluid is doubled while the height of the fluid column remains the same, what happens to the pressure at the bottom of the column?

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4. Question

A submarine is initially at a depth where the pressure due to the water column is 2.5 MPa. If the submarine descends to a depth where the pressure is 5.0 MPa, how has the depth of the submarine changed?