Fluid Mechanics - Head Loss Due to Friction

[Mingsliced]

Homework Statement

This is simply a sanity check concerning the system described and attached. My concerns are detailed within my attempts at the solution. Any guidance will be greatly appreciated!

The diagram attached represents a process for which a pump and associated pipe work require to be correctly sized. The liquid is to be pumped from the underground storage vessel which is vented to atmosphere (assume 1 bar pressure) to a pressurised container supported some distance above ground level. The pump is sited at ground level and must be capable of delivering 0.01 m³ s^–1 with a maximum velocity of 1.8 m/s^–1.

Q = 0.01 m³ s^–1
V = 1.8 m/s^–1
D = 90 mm = 0.09 m
Liquid density, ρ = 960 kg m^–3
Liquid viscosity, μ = 0.081 Pa s
L = 27m (from pump) or 32m (total length).

Homework Equations

See below.

The Attempt at a Solution

Calculate Mean Velocity:

U_m = (4 * Q)/(π * D²)

U_m = (4 * 0.01)/(π * 0.09²)

U_m = 1.57 m/s^-1

Calculate Reynolds number:

Re = (U_m * D * ρ)/μ

Re = (1.57 * 0.09 * 960)/0.081

Re = 1675

As the Reynolds number calculated is less than 2000, the flow is assumed streamlined. Therefore I will use the Poiseuille equation to calculate head loss due to friction:

H_f = (32 * μ * L * U_m)/(ρ * G * D²)

H_f = (32 * 0.081 * 32 * 1.57)/(960 * 9.81 * 0.09²)

H_f = 1.707 m

The first issue I am having is the length of pipe to use within the Poiseuille equation. If you look at the diagram, you can see that the pipe length from the pump to the container is 27m whilst the total pipe length for the system is 32m. I have used total pipe length but I am not sure whether you just count the pipe length from the pump to the container, especially as the diagram shows a line break. Clarification of this would be great.

The second issue I'm having is finding minor head losses from the 90° pipe bends, entry to the pipe and exit from the pipe. Do I count the entire system or simply the pipework starting at the pump and ending at the container?

Just very minor problems that need clarifying really, thanks!

 

[SteamKing]

Homework Statement

This is simply a sanity check concerning the system described and attached. My concerns are detailed within my attempts at the solution. Any guidance will be greatly appreciated!

The diagram attached represents a process for which a pump and associated pipe work require to be correctly sized. The liquid is to be pumped from the underground storage vessel which is vented to atmosphere (assume 1 bar pressure) to a pressurised container supported some distance above ground level. The pump is sited at ground level and must be capable of delivering 0.01 m³ s^–1 with a maximum velocity of 1.8 m/s^–1.

Q = 0.01 m³ s^–1
V = 1.8 m/s^–1
D = 90 mm = 0.09 m
Liquid density, ρ = 960 kg m^–3
Liquid viscosity, μ = 0.081 Pa s
L = 27m (from pump) or 32m (total length).

Homework Equations

See below.

The Attempt at a Solution

Calculate Mean Velocity:

U_m = (4 * Q)/(π * D²)

U_m = (4 * 0.01)/(π * 0.09²)

U_m = 1.57 m/s^-1

Calculate Reynolds number:

Re = (U_m * D * ρ)/μ

Re = (1.57 * 0.09 * 960)/0.081

Re = 1675

As the Reynolds number calculated is less than 2000, the flow is assumed streamlined. Therefore I will use the Poiseuille equation to calculate head loss due to friction:

H_f = (32 * μ * L * U_m)/(ρ * G * D²)

H_f = (32 * 0.081 * 32 * 1.57)/(960 * 9.81 * 0.09²)

H_f = 1.707 m

The first issue I am having is the length of pipe to use within the Poiseuille equation. If you look at the diagram, you can see that the pipe length from the pump to the container is 27m whilst the total pipe length for the system is 32m. I have used total pipe length but I am not sure whether you just count the pipe length from the pump to the container, especially as the diagram shows a line break. Clarification of this would be great.

The second issue I'm having is finding minor head losses from the 90° pipe bends, entry to the pipe and exit from the pipe. Do I count the entire system or simply the pipework starting at the pump and ending at the container?

Just very minor problems that need clarifying really, thanks!

Since you want to see if the pump is suitable, you must analyze the suction side of the pump separately from the discharge side. Remember, the pump provides a discharge flow and an increase in head to the system.

If the pump is of the centrifugal type, it is important that the Net Positive Suction Head Available (NPSHA) be greater than the Net Positive Suction Head Required (NPSHR) for the pump.

http://www.electrical4u.com/power-generation/images/fire-tube-boiler.jpg

Having NPSHA > NPSHR ensures the pump will not cavitate during operation.

From the diagram, your pump must have enough suction to lift the fluid at least 3 m vertically out of the storage tank, in addition to overcoming the minor head losses for the suction pipe and fittings.

After the fluid leaves the pump, you want to ensure that enough head is available at the pump discharge to overcome the losses in the discharge piping including what appears to be a 15 m change in elevation.

Since you have checked your flow regime and found it to be laminar, you should be aware that tables of fitting losses for various pipe fittings are generally compiled for the fully turbulent flow regime and may not be accurate for laminar flow. Researchers have developed new tables and methods for assessing head losses for laminar flow in pipelines as discussed here:

http://www.eng-tips.com/viewthread.cfm?qid=135792

http://www.katmarsoftware.com/articles/pipe-fitting-pressure-drop.htm

 

[Mingsliced]

Thanks very much!