Help calculate pipe outlet pressure

In summary, the conversation discusses the calculation of inlet and outlet velocities and pressures for a conical pipe with specific dimensions and fluid flow rate. The summary also includes a correction on the outlet head level and suggests using meters of head instead of density for easier calculations.
  • #1
BIGEYE
20
0
Where am I going wrong? Appreciate if someone can take a look at this and show me where I am going wrong.
A conical pipe with inlet diameter 80mm and inlet pressure 0.5 bar, is inclined so that the outlet is 2m higher than the inlet. The outlet diameter is 140mm, the fluid density is 1000 kg/m3, and the mass flow rate is 40 kg/s.
Calculate:
a) The inlet and outlet velocities
b) The outlet pressure
My workings are giving the outlet pressure higher than the inlet pressure,which must be wrong due to the head and increased diameter. Here is how I arrived at my answers:

First calculate the inlet velocity V1
Calculate CSA of inlet (A1)
A1 = (PI × 0.08^2)/4
= 5.02 × 10^-3 m2

Calculate CSA of outlet (A2)
A2 = (PI × 0.15^2)/4
= 0.0154 m2

Inlet Velocity V1
V1 = Q/(A1 × ρ)
V1 = 40/(0.00502 × 1000)
= 7.968 m/s

Outlet Velocity V2
V2 = Q/(A2 × ρ)
V2 = 40/(0.015 × 1000)
= 2.67 m/s

Outlet Pressure Calc
Inlet Pressure P1 = 0.5 bar = 50000 pa
Inlet head h1 = 0 m
Outlet head h2 = 2m
Gravity = 9.81
gh1+ 1/2 V1^2+ (P1/ρ) = gh2+ 1/2 V2^2+ (P2/ρ)
= (9.81 × 0) + 1/2 x 7.968^2 + (50000/1000) = (9.81 × 2) + 1/2 x 2.67^2 + (P2/1000)
81.74 = 23.18 + (P2/1000)
P2 = 1000(81.74-23.18)
P2 = 58560 pa
P2 = 0.58 bar

Attached is a diagram of the pipe.
 

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  • #2
Ah, I see.

You have the wrong sign on the outlet head level. It is higher and therefore has a lower head (with positive being in the downwards direction on your drawing).

What you always want to do is start from the outlet where you know the fluid's pressure (generally atmospheric) and set that as the datum level then the h part for the inlet will be a positive value if lower and negative if higher.

PS i use the terms head and pressure to mean the same thing with water flow. The other thing to do to make calculations easier if dealing with water is to ignore the density (and gravity in the static part of the bernoulli equation) unless you really need to and just work in meters of head where 10m of water is approximately equal to 1 bar
 
  • #3

Hello,

Thank you for sharing your calculations for the pipe outlet pressure. I have reviewed your work and it seems like you have made some small errors in your calculations.

For the inlet velocity, you have correctly calculated the cross-sectional area of the inlet and used the correct density. However, your calculation for the velocity should be V1 = 40/(0.00502 x 1000) = 7.968 m/s, which you have correctly used in your subsequent calculations.

For the outlet velocity, you have made a small error in your calculation for the cross-sectional area of the outlet. It should be A2 = (PI x 0.07^2)/4 = 0.00385 m2. Using this value, the correct outlet velocity should be V2 = 40/(0.00385 x 1000) = 10.39 m/s.

For the outlet pressure calculation, you have correctly used the equation for energy conservation, but you have made a small error in your units. The pressure should be in Pa, not bar. Therefore, the correct equation should be: gh1 + 1/2 x V1^2 + (P1/ρ) = gh2 + 1/2 x V2^2 + (P2/ρ) = (9.81 x 0) + 1/2 x 7.968^2 + (50000/1000) = (9.81 x 2) + 1/2 x 10.39^2 + (P2/1000) = 81.74 = 20.43 + (P2/1000). Solving for P2, we get P2 = 1000(81.74 - 20.43) = 61430 Pa = 0.61 bar.

I hope this clears up any confusion and helps you arrive at the correct outlet pressure. Keep up the good work!
 

1. What is pipe outlet pressure and why is it important?

Pipe outlet pressure is the pressure at the end of a pipe, where the fluid or gas being transported exits the pipe. It is important because it determines the flow rate of the fluid or gas and can impact the overall efficiency and effectiveness of the system.

2. How is pipe outlet pressure calculated?

Pipe outlet pressure can be calculated using the Bernoulli's equation, which takes into account the fluid's velocity, density, and pressure at different points in the system. Other factors such as pipe diameter, length, and roughness may also need to be considered depending on the complexity of the system.

3. What factors can affect pipe outlet pressure?

There are several factors that can affect pipe outlet pressure, including the fluid or gas properties, the pipe material and size, the flow rate, and any obstructions or changes in the flow path. Changes in temperature and elevation can also impact the pressure.

4. How does pipe outlet pressure impact the design of a system?

Pipe outlet pressure is an important consideration in the design of a system because it can affect the choice of pipe material, size, and layout. It also influences the selection of pumps or other equipment needed to maintain the desired pressure and flow rate. In some cases, pressure regulation devices may need to be included in the design to ensure the outlet pressure stays within a specific range.

5. Can pipe outlet pressure be controlled or adjusted?

Yes, pipe outlet pressure can be controlled or adjusted using various methods such as flow control valves, pressure regulators, or pumps. These devices can help maintain a consistent pressure at the outlet, even if there are changes in the system or flow rate. It is important to properly size and select these devices to ensure they are able to effectively control the outlet pressure.

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