How Do I Solve These Challenging Fluid Mechanics Problems?

[Proleague]

I stucked with my hard fluid questions. I don't know what should I do first.
So, Please describe detail as much as possible.
Thanks for Physics Genious guys.


2. A house at the bottom of a hill is fed by a full tank of water 5.0m deep and connected to the house by a pipe that is 110m long at an angle of 58 degree from the horizontal. (a) Determine the water gauge pressure at the house. (b) How high could the water shoot if it came vertically out of a broken pipe in front of the house?

what should I use equation for (a) and how it works for (b)


3. A spherical balloon has a radius of 7.35m and is flled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930kg? Neglect the buoyant force on the cargo volume itself.

So F(b) = (mass of helium + mass of cargo) X 9.8

F(b) = Density of air X volume X 9.8

9.8 cancels out on both sides.

Density of air is 1.29 kg/m^3 so
1.29V = (mass of helium + mass of cargo)

I cannot go further after this step. Please answer what should I do for next, and please let me know that if I am wrong for some equation during the process.

 

[jbsteele]

To solve this problem, you will need to use the equation for the volume of a sphere, which is V = (4/3)πr^3. Substitute the given values for r and calculate the volume of the balloon. Then, subtract the mass of the helium and the skin and structure of the balloon from the total mass that the balloon can lift to get the mass of the cargo that it can lift.

 

[tomcue]

I understand that fluid mechanics can be a challenging subject and it is common to get stuck on difficult questions. My first recommendation would be to review the basic concepts of fluid mechanics, such as Pascal's law, Bernoulli's principle, and the continuity equation. These concepts will help you understand the underlying principles behind the equations you will use to solve the problems.

For the first question, you can use the equation P = ρgh to calculate the water gauge pressure at the house, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column. In this case, h would be the difference in height between the surface of the water in the tank and the pipe at the house. You can then use trigonometry to find the actual height of the water column in the pipe.

For the second question, you can use the same equation, P = ρgh, to calculate the pressure at the broken pipe. Since the pipe is broken, the pressure would be atmospheric pressure, which is approximately 1 atm. You can then use this pressure and the density of air to find the height that the water would shoot if it came out vertically from the pipe.

For the third question, you are on the right track. The buoyant force on the balloon is equal to the weight of the air it displaces, which is equal to the weight of the helium and cargo combined. So, you can set the buoyant force equal to the weight of the balloon and cargo and solve for the mass of the cargo. Keep in mind that the mass of the helium and cargo will be equal to the volume of the balloon (using the density of helium) plus the mass of the cargo, which is what you calculated in your equation. I would recommend reviewing the concept of buoyancy and how it relates to the weight of displaced fluid.

I hope this helps and best of luck with your fluid questions! Remember to always review the basic concepts and equations before attempting to solve the problems. And don't be afraid to ask for help from your peers or professors if you are still stuck. Keep up the good work and continue being a physics genius!