Hydrostatic pressure in the Bernoulli Equation

In summary, the hydrostatic pressure term in the Bernoulli equation decreases with fluid depth due to the selection of a coordinate system where the vertical direction faces up instead of down. This has physical significance in terms of the direction in which objects will naturally move in the fluid.
  • #1
JJBladester
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Homework Statement



The hydrostatic pressure term in the Bernoulli equation (ρgz) decreases with fluid depth. Why?

Homework Equations



Bernoulli Equation (multiplied by density ρ to give us pressure units):

[tex]P+\rho\frac{V^2}{2}+\rho gz=constant[/tex]

The Attempt at a Solution



In the hydrostatics chapter in my book, hydrostatic pressure, ρgh, increases with depth. However, in the Bernoulli equation, the hydrostatic pressure term ρgz decreases with depth.

Is this just because we're selecting a coordinate system where the vertical direction faces up instead of down?

What physical significance does this have?
 
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  • #2
Hi JJBladester! :smile:
JJBladester said:
Is this just because we're selecting a coordinate system where the vertical direction faces up instead of down?

Yes, h = -z. :wink:
What physical significance does this have?

erm :redface: … swim the way the bubbles go? o:)
 

Related to Hydrostatic pressure in the Bernoulli Equation

1. What is hydrostatic pressure in the Bernoulli Equation?

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it. In the Bernoulli Equation, it represents the potential energy of the fluid due to its position in a gravitational field.

2. How does hydrostatic pressure affect fluid flow in the Bernoulli Equation?

Hydrostatic pressure is one of the terms in the Bernoulli Equation that contributes to the total energy of a fluid. It represents the potential energy of the fluid, and as the fluid flows through a constriction, the hydrostatic pressure decreases, causing an increase in velocity and kinetic energy.

3. Can hydrostatic pressure be neglected in the Bernoulli Equation?

In some cases, hydrostatic pressure can be neglected if the fluid is moving at high velocities or if the change in elevation is small. However, in most real-world situations, it is important to consider hydrostatic pressure in the Bernoulli Equation to accurately model fluid flow.

4. How is hydrostatic pressure calculated in the Bernoulli Equation?

Hydrostatic pressure is typically calculated using the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column. This value can then be substituted into the Bernoulli Equation.

5. What are some applications of the Bernoulli Equation and hydrostatic pressure?

The Bernoulli Equation and hydrostatic pressure have many practical applications, such as calculating water pressure in pipes, designing airfoils for aircraft, and understanding blood flow in the human body. They are also important in fields such as fluid mechanics, aerodynamics, and hydraulics.

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