I’m quite confused on what the static pressure P is in Bernoulli’s equation. I’m not sure if it’s the external pressure causing fluid to move through, let’s say, a pipe, or the internal pressure within the fluid that’s moving in all the directions.
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It’s the pressure in the liquid. Suppose your pipe had a small hole in it with a tall vertical tube attached. The liquid from the pipe would obviously go into the tube as well and rise to a certain height defined by when the pressure exerted by the column of liquid in the tube becomes equal to the pressure in the pipe (minus atmospheric pressure of course). That value is the static pressure at that point in the pipe where the hole is.
The word “static” is used to discern it from dynamic pressure which is basically the kinetic energy per unit volume of the flowing liquid. Otherwise “static pressure” and “pressure” are synonyms.
In Bernoulli’s equation, the static pressure P is the pressure of the fluid when it is not moving or when it is moving at a constant velocity. This is the pressure that the fluid exerts on the walls of a pipe or other container when it is not flowing or when it is flowing at a constant speed. The dynamic pressure is the pressure of the fluid when it is moving and its velocity is changing. This is the pressure that the fluid exerts on the walls of a pipe or other container when it is flowing and its speed is increasing or decreasing.
It’s just a known pressure. (rho x g xh)
If you started at sea level, and climbed 30m up a hill, you can poke a flag in the ground that lets you know this is a known elevation (P). So later if you want to measure higher elevations on a hill, you can just start from your known 30m flag and go from there. So now if you climb 50m up from that flag, you know you are at P+50m. (80m).
The P1 in Bernoulli’s Eq is just a flag with a known pressure; an anchor point that lets you calculate P2, the pressure you want.
P1 can be any known pressure in your system. Even right on the surface, at zero.
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r/ShaemusOdonnelly answered this correctly, but he might be getting downvoted, I can’t tell.
OP, what you described as internal pressure is indeed static pressure. 👍🏼
Source: PhD in Aeronautics.
Those aren’t two different things. That’s the point. Pressure is the force exerted outwards in all directions and is the force exerted on the fluid causing it to move, and these two seemingly contrary forces aren’t just always balanced quantitatively they are *literally the same*. For a fluid in a pipe, for instance, the “external” pressure pushes on the fluid, and this causes the fluid to push against everything else in all directions, including both the pipe (which resists that pressure if it has sufficient structural integrity) and the “open” end of the pipe, causing the fluid to flow away from the source of that pressure (which includes all the other fluid pushing against it…)
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