Bernoulli's Equation and pressure differences

In summary, Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height of a fluid at different points along a streamline. It can be used to calculate pressure differences between two points in a fluid flow and is applicable to all fluids, but only if they are incompressible and free from friction and viscosity. Some real-world applications of Bernoulli's equation include aircraft design and water flow calculations. However, it has limitations such as assuming steady flow and not accounting for turbulence and compressibility.
  • #1
OnAHyperbola
29
12

Homework Statement


Problem in attached image

Homework Equations



$$P_1+\frac{\rho v_1^2}{2}=P_2+\frac{\rho v_2^2}{2}$$
bernoulii.PNG

The Attempt at a Solution


I understand everything in the solution except why $$P_A-P_B=h(\rho_{Hg}-\rho)g$$ Why do we have to subtract the density of water from that of mercury instead of just taking the density of mercury??

Any help is appreciated.
 
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  • #2
Consider starting at point B and moving down through the U-tube all the way around until you come up the left side of the U-tube to point A. Keep track of all the pressure changes.
 

1. What is Bernoulli's Equation?

Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height of a fluid at different points along a streamline. It states that the sum of the kinetic energy, potential energy, and pressure energy of a fluid is constant along a streamline.

2. How is Bernoulli's Equation used to calculate pressure differences?

Bernoulli's equation can be rearranged to calculate pressure differences between two points in a fluid flow. By equating the total energies at two points along a streamline, the difference in pressure can be found.

3. Can Bernoulli's Equation be applied to all fluids?

Bernoulli's equation is applicable to all fluids, both liquids and gases. However, it assumes that the fluid is incompressible and that there is no friction or viscosity present.

4. What are some real-world applications of Bernoulli's Equation?

Bernoulli's equation has many practical applications, such as in the design of aircraft wings and propellers, the calculation of water flow in pipes and channels, and the operation of carburetors and atomizers.

5. Are there any limitations to using Bernoulli's Equation?

While Bernoulli's equation is a useful tool, it does have some limitations. It assumes that the fluid is in steady flow, which may not always be the case. It also does not take into account factors such as turbulence and compressibility, which can affect the accuracy of the calculations.

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