# What does the pressure term in Bernoulli's equation signify?

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?

• Hi, I would suggest making your question more closed by including the formula in the question. This can be done by enclosing the equation in double dollar-signs. – Kraig Jun 17 at 18:20
• Suppose you use a traditional mercury barometer: you have a glass tube in a U shape which is closed on one end, you fill it from the closed end with mercury and then carefully turn it over so that the mercury on the closed end draws a vacuum which pulls it upwards, so that it remains many millimeters above the line of mercury on the open end. This thing measures pressure. Does it only measure pressure "due to height"? – CR Drost Jun 17 at 18:22
• So you know what pressure is, but you're asking specifically how to interpret pressure in the context of Bernoulli's equation? – Nat Jun 17 at 19:31
• – Kyle Kanos Jul 31 at 12:33

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.

Pressure is a force per unit area, how it is generated may or may not be relevant.

I would prefer an elephant to stand on my foot than a lady with a stiletto heel...

• This is very brief. The first sentence is ambiguous, and the second sentence doesn't seem very relevant or helpful. – Ben Crowell Jul 30 at 20:49