# Split Pipe Flow: Multiple Inlets and Outlets (Bernoulli's)

• CollegeCourt
In summary, the problem involves using Bernoulli's equation and the equation for conservation of mass to solve for the unknown volumetric flows and pressures in a system of simultaneous equations.
CollegeCourt
http://tinypic.com/view.php?pic=mhvarc&s=9#.WD__u_mLTIU Hey guys,
So, I've got this problem, attached.
I've used Bernoulli's to produce P1 + (1/2)p(u1)^2 +P2 + (1/2)p(u2)^2 = P3+ (1/2)p(u3)^2 +P4 + (1/2)p(u4)^2 +P5 + (1/2)p(u5)^2,
Plugging in the values you get 82500 + P2 + 500(u2)^2 = P3 + 60000 + 500(u4)^2 + P5 + 500(u5)^2
Replacing velocity with volumetric flow/area,
82500 + P2 + 500(Q2/A2)^2 = P3 + 500(Q4/0.03)^2 + P5 + 500(0.74/(A5)^2
Now I know Q1 + Q2 = Q3 +Q4 + Q5, but I have come to a dead end. Is this just numerous simultaneous equations or is there another way about this?
https://postimg.org/image/gqfk1aukn/

Thanks!

Yes, this is a system of simultaneous equations. You will need to use the equation for conservation of mass to determine the unknown volumetric flows (Q2, Q4, and Q5). This equation states that the sum of all volumetric flows at any given point in the system must equal the volumetric flow at the next point. From this, you can solve for Q2, Q4, and Q5. Once you have these values, you can then plug them into your Bernoulli equation and solve for the pressures.

## 1. What is split pipe flow?

Split pipe flow refers to the flow of a fluid through a pipe that splits into multiple branches with different inlet and outlet conditions.

## 2. What is Bernoulli's principle and how does it relate to split pipe flow?

Bernoulli's principle states that in an ideal fluid flow, the sum of kinetic energy, potential energy, and pressure energy remains constant. In split pipe flow, the different inlet and outlet conditions result in changes in pressure, which can be explained by Bernoulli's principle.

## 3. How do you calculate the flow rate in a split pipe system?

The flow rate in a split pipe system can be calculated using the continuity equation, which states that the mass flow rate in a pipe is constant. This equation takes into account the cross-sectional area, velocity, and density of the fluid in each branch of the split pipe system.

## 4. What factors can affect the flow distribution in a split pipe system?

The flow distribution in a split pipe system can be affected by factors such as the diameter and length of the pipes, the fluid properties, the inlet and outlet conditions, and any obstructions or bends in the pipes.

## 5. How can split pipe flow be useful in practical applications?

Split pipe flow is commonly used in industrial and engineering applications where different flow rates or pressures are required at various points in a system. It can also be used in hydraulic systems, heating and cooling systems, and in the design of piping networks for efficient fluid flow.

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