About this video
This short lesson gives the formula for absolute pressure at a depth h in a fluid, P = P0 + rho g h, where P0 is atmospheric pressure. It then rearranges the formula step by step to solve for depth, h = (P - P0) / (rho g), and shows why each algebra step is valid.
You'll be able to
- identify each symbol in the absolute pressure formula.
- rearrange P = P0 + rho g h to solve for depth h.
- predict how changing fluid density affects the depth needed for a given pressure.
Key words
- Absolute pressure
- The total pressure at a point in a fluid, including the pressure of the atmosphere above it.
- Atmospheric pressure (P0)
- The pressure of the air above the fluid's surface, here written as P sub zero.
- Density (rho)
- The mass of a substance per unit volume, written here as the Greek letter rho.
- Gravitational acceleration (g)
- The rate at which gravity speeds up falling objects, about 9.8 m/s squared on Earth.
- Depth (h)
- How far below the fluid's surface a point is located.
Transcript
- [Instructor] The absolute pressure P in a fluid of density rho, I know this looks like a lowercase p but this is the Greek letter rho, which we typically use for density, at a given depth h can be found with the above equation where capital P with the little subscript of this, I guess P sub zero, or maybe it's just an O but it looks like a zero, P sub zero is atmospheric pressure and g is gravitational acceleration.
Which of the following is the correct expression for the depth in terms of the absolute pressure, atmospheric pressure, fluid density, and gravitational acceleration? So essentially what we wanna do is we wanna solve for depth, we wanna solve for h. So let's see if we can do that.
So we have P is equal to P sub, I'll call this P sub zero, plus rho times g times h. Now to solve for h, I would at least wanna isolate this term that contains h on the right-hand side and so let me subtract P sub zero from both sides. So subtract P sub zero, subtract P sub zero, and then on the left-hand side, I have capital P minus capital P sub zero is equal to, those are going to cancel out.
You're gonna have rho times g time h and now to solve for h I can divide both sides by rho times g, so let's do that. Let's divide this side by rho times g and let's divide this side by rho times g. Rho times g divided by rho times g is just going to be one and we get h is equal to this thing right over here.
We could say h is equal to capital P minus capital P sub zero over rho times g, and that is the first choice right over there.
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