# Fluids: Energy equation involving head loss

• reddawg
In summary: If P is absolute pressure, then the tank cannot exhaust to atmosphere, since the pressure there > the supposed pressure inside the tank.
reddawg

## Homework Statement

See attached image:

## Homework Equations

p/ρg + V^2/2g + z = constant

head loss (major) = f * l/D * V^2/2g

## The Attempt at a Solution

To use the energy equation while incorporating head loss, I need to determine the velocity in each section of pipe. The problem is I don't know how! I do know that the pressure drop from the tank to the atmosphere is equal to the pressure in the tank.

#### Attachments

• problem1.JPG
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The frictional term has to be properly combined with the bernoulli equation. To get you started, let Q represent volumetric throughput rate. This is what you will be solving for. In terms of Q, what is the velocity of the air in each of the sections. From the ideal gas law, what is the density of the air?

Chestermiller said:
The frictional term has to be properly combined with the bernoulli equation. To get you started, let Q represent volumetric throughput rate. This is what you will be solving for. In terms of Q, what is the velocity of the air in each of the sections. From the ideal gas law, what is the density of the air?
V is equal to the flowrate Q divided by the cross-sectional area of each pipe.

From the ideal gas law, density ρ = p/RT = 6.88*10^-5 slugs/ft^3

reddawg said:
V is equal to the flowrate Q divided by the cross-sectional area of each pipe.

From the ideal gas law, density ρ = p/RT = 6.88*10^-5 slugs/ft^3

You have to be careful with units here, especially R for air.

Can you show your calculation of ρ in detail?

SteamKing said:
You have to be careful with units here, especially R for air.

Can you show your calculation of ρ in detail?
ρ = (.5 psi)(144 in2/ft2) / (1716)(609.7)
1716 is R in British units
609.7 is 150 degrees f converted to rankine

reddawg said:
ρ = (.5 psi)(144 in2/ft2) / (1716)(609.7)
1716 is R in British units
609.7 is 150 degrees f converted to rankine
Is P = 0.5 psi absolute or gage reading?

The units of R here are ft-lbf / slug-°R to be precise.

SteamKing said:
Is P = 0.5 psi absolute or gage reading?

The units of R here are ft-lbf / slug-°R to be precise.
Yes, I agree with those units. And P is absolute pressure I think.

reddawg said:
Yes, I agree with those units. And P is absolute pressure I think.
If P is absolute pressure, then the tank cannot exhaust to atmosphere, since the pressure there > the supposed pressure inside the tank.

## 1. What is the energy equation involving head loss?

The energy equation involving head loss is a fundamental equation in fluid mechanics that governs the transfer of energy within a fluid system. It states that the total energy at any point in the system is equal to the sum of the kinetic energy, potential energy, and the energy lost due to friction or head loss.

## 2. How is head loss calculated?

Head loss is calculated using the Darcy-Weisbach equation, which relates the head loss to the friction factor, pipe length, diameter, and flow rate. The equation can also be simplified for certain flow regimes, such as laminar or turbulent flow.

## 3. What factors can cause head loss in a fluid system?

Head loss in a fluid system can be caused by a variety of factors, including pipe roughness, changes in elevation, flow rate, and fluid viscosity. Other factors such as fittings, bends, and valves can also contribute to head loss.

## 4. How does head loss affect the performance of a fluid system?

Head loss can significantly affect the performance of a fluid system by decreasing the total energy available for the fluid to flow through the system. This can result in decreased flow rates, increased pumping power requirements, and reduced efficiency of the system.

## 5. How can head loss be minimized in a fluid system?

Head loss can be minimized by using smoother pipes, minimizing the number of fittings and bends, and reducing the flow rate. Additionally, choosing the appropriate pipe diameter, fluid viscosity, and flow regime can also help to reduce head loss in a fluid system.

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