How Does Bernoulli's Principle Apply to Fluid Flow in Pipes?

In summary, a large water tank has an inlet pipe and an outlet pipe with different diameters and heights. A certain volume of water enters the tank every minute at a specific pressure. Using the equation for fluid dynamics, the velocity of the water in the outlet pipe is determined to be 4.943 m/s. However, the gauge pressure in the outlet pipe remains unknown.
  • #1
brv
2
0

Homework Statement



A large water tank has an inlet pipe and an outlet pipe. The inlet pipe has a diameter of 1.89 cm and is 1.29 m above the bottom of the tank. The outlet pipe has a diameter of 5.47 cm and is 4.25 m above the bottom of the tank. A volume of 0.697 m3 of water enters the tank every minute at a gauge pressure of 1 atm.

a) What is the velocity of the water in the outlet pipe?
4.943 m/s

b)What is the gauge pressure in the outlet pipe?

Homework Equations





The Attempt at a Solution



a) What is the velocity of the water in the outlet pipe?
4.943 m/s

I found this part but i don't know how to do the second part.Please help me.
 
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  • #2
brv said:

Homework Statement



A large water tank has an inlet pipe and an outlet pipe. The inlet pipe has a diameter of 1.89 cm and is 1.29 m above the bottom of the tank. The outlet pipe has a diameter of 5.47 cm and is 4.25 m above the bottom of the tank. A volume of 0.697 m3 of water enters the tank every minute at a gauge pressure of 1 atm.

a) What is the velocity of the water in the outlet pipe?
4.943 m/s

b)What is the gauge pressure in the outlet pipe?

Homework Equations




The Attempt at a Solution



a) What is the velocity of the water in the outlet pipe?
4.943 m/s

I found this part but i don't know how to do the second part.Please help me.

What equation is commonly used in fluid dynamics questions?
 

Related to How Does Bernoulli's Principle Apply to Fluid Flow in Pipes?

What is the Bernoulli equation?

The Bernoulli equation is an important equation in fluid dynamics that relates the pressure, velocity, and height of a fluid at any point along a streamline. It is based on the principle of conservation of energy, and is often used to analyze fluid flow in various applications.

What is the significance of the Bernoulli equation?

The Bernoulli equation is significant because it allows us to understand and predict the behavior of fluids in various systems, such as in pipes, pumps, and wings of airplanes. It also helps us to calculate the flow rate and pressure changes in these systems, making it a valuable tool in engineering and science.

What is the formula for the Bernoulli equation?

The formula for the Bernoulli equation is P + 1/2ρv² + ρgh = constant, where P is the pressure, ρ is the density of the fluid, v is the velocity, g is the acceleration due to gravity, and h is the height of the fluid.

How is the Bernoulli equation derived?

The Bernoulli equation is derived from the principle of conservation of energy, which states that the total energy of a closed system remains constant. By applying this principle to a fluid flowing along a streamline, we can derive the Bernoulli equation by considering the changes in kinetic energy, potential energy, and pressure energy of the fluid.

What are the assumptions made in the Bernoulli equation?

The Bernoulli equation makes the following assumptions:

  • The fluid is incompressible and non-viscous
  • The flow is steady and along a streamline
  • The effects of gravity are negligible
  • The fluid is an ideal fluid (no friction or energy losses)
These assumptions allow us to simplify the equation and make it easier to use in practical applications.

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