If I have a pipe for which I know the height and velocity of the fluid at the left and right end, and I am asked to find the gauge pressure at the right end, how would I go about doing this if the internal pressure at both ends is unknown to me? I am aware that finding the difference in pressures will give me the correct answer, though I dont necessarily understand why this is the same thing as P(g) = P(abs) – P(atm). It just doesn't intuitively make sense to me. Any explanation would be much appreciated. Thanks!!
[Physics] How to find gauge pressure in pipe
fluid dynamicsgaugepressure
Related Solutions
Your way is correct. About your doubt it's important to see the two points on the streamline where you want to apply the Bernoulli Equation. Taking point just inside and just outside the the pipe will matter a lot.
$P_1=0 $ when the second point you choose the point outside the pipe ,which is open to vacuum so pressure is zero. Whereas if you choose a point just inside the pipe at the bottom of the tank the pressure is $P_1=P_0+\rho g h$ .Also this case will give us the velocity of water at the bottom of tank and not the velocity of water leaving the pipe .
Also pressure is a scalar and can be seen as $$P=\dfrac{\vec F.\vec A}{|\vec A|^2}$$ Where area vector is a vector pointing perpendicular to the arwa of the surface and $|A|$=area of surface
$F$ is the sum of two forces - the inward force at the start and the smaller inward force at the end. Since they act in opposite directions, it's also the difference in the magnitudes of the forces which directly corresponds to the difference in pressures. Eg if there's 5.0 atm at the start and 4.0 atm at the end, then $$ F = F_{start} + F_{end} $$ $$ =({5.0 \space atm \times A}) + - ({4.0 \space atm \times A}) $$ $$ = \Delta P \times A $$ $$ = 1.0 \space atm \times A $$
In the special case where the water is released into a vacuum, then $F_{end} = 0$ and you don't need to use any differences.
Best Answer
If the right end is open to the atmosphere, then the gauge pressure is zero, and the absolute pressure at the right ends is equal to atmospheric pressure.