# Fluid Mechanics Help: Find Balloon Radius & Pipe Flow Rate

• eutopia
In summary: And in this case, mass of the balloon is what we are trying to solve for. In summary, a spherical helium-filled balloon is used to lift a load of 5905 N (in addition to the weight of the helium). To find the minimum necessary radius for the balloon, we must calculate the buoyant force (B = pVg) and set it equal to the weight of the displaced air (5905 N) plus the weight of the balloon and load. This allows us to solve for the spherical balloon radius. In the second problem, we must use the Ideal Gas Law to calculate the final pressure in a container filled with 5.7 grams of water at 115.8 degrees Celsius. In the last problem
eutopia
A spherical helium-filled balloon is used to lift a load of 5905 N (in addition to the weight of the helium). Suppose the density of the air is 1.24 kg/m3. Find the minumum necessary radius for the balloon.

A 24.8 liter container is initially evacuated, and then 5.7 grams of water is placed in it. After a time, all the water evaporates, and the temperature is 115.8o C. Find the final pressure.

A water tower, vented to the atmosphere, is drained by a pipe that extends to the ground. The top surface of the water in the tank is 15.7 m above the ground. If the valve in the drain pipe is closed, what is the absolute pressure in the drain pipe at ground level?
Answer: 2.55E5 Pa
If the valve is now open and the cross-sectional area of the drain pipe is 2.24E-2 m2, find the volume flow rate in the drain pipe. Assume that the water speed at the top of the water in the tank is negligible.

Last edited:
show some work?

I don't really know how to approach the first and second problem... like how to set up the equations or which one to use.

For the last one, volume flow rate = area x velocity, so I tried to find the velocity with Bernoulli's equation, but I didn't know how the variables are set up with it.

P1 + (1/2)pv1^2 + pgy1 = P2 + (1/2)pv2^2 + pgy2

if P1 is the atmosphere pressure, then P2 is the pressure at the bottom of the pipe. since the velocity is neglible at the top, and at the bottom y2 becomes 0

P1 + pgy1 = P2 + (1/2)pv2^2... but then, if P2 already = P1 + pgy1.. then there would be no velocity... so I'm kind of confused.

Well You know where you would get the radius right? From the Volume of the Sphere, but first you need to set up the equation for the [load+balloon] system.

$$\vec{B} + \vec{W}_{balloon+load} = 0$$

Now express in terms you can work out.

Last edited:
eutopia said:
A water tower, vented to the atmosphere, is drained by a pipe that extends to the ground. The top surface of the water in the tank is 15.7 m above the ground. If the valve in the drain pipe is closed, what is the absolute pressure in the drain pipe at ground level?
Answer: 2.55E5 Pa
If the valve is now open and the cross-sectional area of the drain pipe is 2.24E-2 m2, find the volume flow rate in the drain pipe. Assume that the water speed at the top of the water in the tank is negligible.

I don't really know how to approach the first and second problem... like how to set up the equations or which one to use.

For the last one, volume flow rate = area x velocity, so I tried to find the velocity with Bernoulli's equation, but I didn't know how the variables are set up with it.

P1 + (1/2)pv1^2 + pgy1 = P2 + (1/2)pv2^2 + pgy2

-------------

if P1 is the atmosphere pressure, then P2 is the pressure at the bottom of the pipe. since the velocity is neglible at the top, and at the bottom y2 becomes 0

P1 + pgy1 = P2 + (1/2)pv2^2... but then, if P2 already = P1 + pgy1.. then there would be no velocity... so I'm kind of confused.
When the valve is opened, the situation becomes {P2 = P1}. Recalculate your results using this fact together with the other given values.

~~

Cyclovenom said:
Well You know where you would get the radius right? From the Volume of the Sphere, but first you need to set up the equation for the [load+balloon] system.

$$\vec{B} + \vec{W}_{balloon+load} = 0$$

Now express in terms you can work out.

... I know the weight of the ballon, but what would the weight of the helium be? and what would B represent here?

When the valve is opened, the situation becomes {P2 = P1}. Recalculate your results using this fact together with the other given values.
Thanks! It makes sense now that I think about it.

eutopia said:
A 24.8 liter container is initially evacuated, and then 5.7 grams of water is placed in it. After a time, all the water evaporates, and the temperature is 115.8o C. Find the final pressure.
{Volume of Container} = V = (24.8 liter)
{Moles of Water in Container} = n = (5.7 grams)/(18 grams/mole) = (0.3167 moles)
{Temperature} = T = (115.8 degC) = (388.9 degK)
{Ideal Gas Constant} = R = (0.08206 Liter*atm/(mol*degK))

Use the Ideal Gas Law to calculate Pressure "P" in units of "atmospheres":
P*V = n*R*T

~~

xanthym said:
{Volume of Container} = V = (24.8 liter)
{Moles of Water in Container} = n = (5.7 grams)/(18 grams/mole) = (0.3167 moles)
{Temperature} = T = (115.8 degC) = (388.9 degK)
{Ideal Gas Constant} = R = (0.08206 Liter*atm/(mol*degK))

Use the Ideal Gas Law to calculate Pressure "P" in units of "atmospheres":
P*V = n*R*T

~~

I tried working with the ideal gas law, but forgot that to get the number of moles, i would take 5.7 and divide that by (1 for hydrogen + 1 hydrogen + 16 for oxygen) ^^ the 5.7 kind of just stared at me

Cyclovenom said:
$$\vec{B} + \vec{W}_{balloon+load} = 0$$

I thought:
density = mass / volume

somehow find the mass of the helium ballon, and then I would get my volume.

But the mass is what got me stuck. Would the weight of the helium equal the weight of the load?... how else would you find the weight of the helium... and what does B stand for in the above equation?

weight of helium + weight of balloon = weight of displaced air

density of helium = .179
density of air = 1.24

eutopia said:
weight of helium + weight of balloon = weight of displaced air

density of helium = .179
density of air = 1.24
Now solve the equation for spherical balloon radius "R":
{Weight of Helium} + {Weight of Balloon + Load} = {Weight of Displaced Air} ::: <--- Buoyant Force
::: ⇒ {ρhelium*Vballoon*g} + {5905 N} = {ρair*Vballoon*g}
::: ⇒ {ρhelium*(4*π*R3/3)*g} + {5905 N} = {ρair*(4*π*R3/3)*g}

~~

Last edited:
Eutopia, i meant what Xanthym said. B stands for buoyant force, remember we consider air a fluid.

$$F = pVg$$

I guess that was the key formula I was missing

but then again

$$pV = m$$!

## What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids and how they behave when subjected to different forces. It involves the study of fluid properties, such as density and viscosity, and how they affect the movement of fluids in different systems.

## How do you find the radius of a balloon using fluid mechanics?

The radius of a balloon can be found by using the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and the number of particles present. By measuring the pressure and temperature of the gas inside the balloon, and knowing the number of particles present, the radius of the balloon can be calculated.

## What is pipe flow rate in fluid mechanics?

Pipe flow rate is a measure of the volume of fluid that is flowing through a pipe per unit time. It is affected by factors such as the diameter of the pipe, the pressure difference between the two ends of the pipe, and the viscosity of the fluid.

## How is the pipe diameter related to the flow rate?

The pipe diameter has a direct impact on the flow rate. A larger diameter pipe will have a higher flow rate compared to a smaller diameter pipe, as it allows for more fluid to pass through in a given amount of time.

## What are common applications of fluid mechanics in everyday life?

Fluid mechanics has many practical applications in everyday life, such as in the design of pipes and pumps for water distribution systems, the aerodynamics of cars and airplanes, and the study of blood flow in the human body. It also plays a role in industries such as oil and gas, chemical processing, and environmental engineering.

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