Consider the Bernoulli equation of fluid dynamics. One of the terms is $p$. I know it is pressure. But what type of pressure is it? Is it pressure due to height or a completely different concept?
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The Bernoulli equation is normally stated as:
$P_1 + 1/2 \rho v_1^2 + \rho g h_1 = P_2 + 1/2 \rho v_2^2 + \rho g h_2$
Obviously, there is a pressure term on both sides of the equal sign. In addition to that, the equation must be dimensionally consistent, so each term in the Bernoulli equation must have the same dimensions.
To discern what pressure means in this equation, it is convenient to work with one of the "non pressure" terms. Thus, the term $\rho g h$ can be manipulated as follows, to illustrate an alternative view of what the pressure term actually represents.
$\rho g h = (m/V) g h$
$\rho g h = (mgh/V)$
Since $mgh$ is equal to gravitational potential energy, it is readily seen that each term in the Bernoulli equation is equivalent to energy per unit volume, including the pressure term.
Regarding what type of term pressure is, consider a pipe with fluid flowing through it. The inlet pressure is $P_1$ and the outlet pressure is $P_2$. Since the fluid flow involves a velocity, and velocity is associated with kinetic energy, there is a term for this, which is the $1/2 \rho v^2$ term. Finally, there is usually a change in height associated with any piping system, so a term is needed in the Bernoulli equation to account for changes in gravitational potential energy, which is what the $\rho g h$ term accounts for. Thus, the Bernoulli equation is actually an energy balance for fluid flow.
David White
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Pressure is a force per unit area, how it is generated may or may not be relevant.
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