Fluid Mechanics HW How pressure in a tank affects exit velocity of a fluid

In summary, according to Bernoulli's principle, the pressure in a tank directly affects the exit velocity of a fluid, as an increase in pressure leads to an increase in exit velocity due to an increase in potential energy. The shape of the tank does not have a direct effect on exit velocity, but can indirectly affect it through changes in pressure. The density of the fluid also indirectly affects exit velocity through changes in pressure. Other factors that can affect exit velocity include viscosity of the fluid, size of the exit opening, and any obstructions in the fluid's path. The Bernoulli's equation can be used to calculate exit velocity based on pressure, density, and height of the fluid.
  • #1
fluidmech
17
1


I'm just a bit lost on how to find the change in pressure. I've posted a picture of my work thus far.
 

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  • #2
Can't read what you wrote but you seem to be on the right track, using Bernoulli.
 
  • #3
I said I was lost and didn't know what to do next..
 
  • #4
fluidmech said:
I said I was lost and didn't know what to do next..

Could you provide a legible description of the problem. Also your effort at solving.
 
  • #5


I can provide some guidance on how to approach this problem. The change in pressure in a tank can be determined by using the Bernoulli's equation, which states that the total energy of a fluid in a closed system remains constant. This equation takes into account the pressure, velocity, and height of the fluid.

To find the change in pressure, you will need to consider the initial pressure in the tank and the exit velocity of the fluid. The exit velocity can be calculated using the continuity equation, which states that the mass flow rate of a fluid remains constant in a closed system.

Once you have determined the exit velocity, you can use the Bernoulli's equation to solve for the change in pressure. This change in pressure will directly affect the exit velocity of the fluid, as stated by the Bernoulli's equation.

I would suggest reviewing your work and ensuring that all the necessary equations and variables are included. Additionally, double-check your calculations to ensure accuracy.

Overall, the relationship between pressure and exit velocity in a tank is a fundamental concept in fluid mechanics and can be solved using established equations and principles. I hope this helps in your understanding and problem-solving process.
 

1. How does pressure in a tank affect the exit velocity of a fluid?

According to Bernoulli's principle, as the pressure in a tank increases, the fluid's exit velocity will also increase. This is because as the pressure increases, the potential energy of the fluid increases, causing it to flow faster when exiting the tank.

2. Is the exit velocity of a fluid affected by the shape of the tank?

No, the shape of the tank does not directly affect the exit velocity of the fluid. However, the shape of the tank can indirectly affect the pressure inside, which in turn will affect the exit velocity.

3. How does the density of the fluid affect the exit velocity?

The density of the fluid does not directly affect the exit velocity. However, it does affect the pressure inside the tank, which will then affect the exit velocity according to Bernoulli's principle.

4. What other factors besides pressure can affect the exit velocity of a fluid in a tank?

Other factors that can affect the exit velocity of a fluid include the viscosity of the fluid, the size of the opening through which the fluid exits, and any obstructions or obstacles in the path of the fluid.

5. How can the exit velocity of a fluid be calculated based on the pressure in a tank?

The exit velocity of a fluid can be calculated using the Bernoulli's equation, which takes into account the pressure, density, and height of the fluid. The equation is v = √(2gh + (P₁-P₂)/ρ), where v is the exit velocity, g is the acceleration due to gravity, h is the height of the fluid, P₁ is the initial pressure in the tank, P₂ is the pressure at the exit point, and ρ is the density of the fluid.

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