# Flow through parallel pipes with different diameters

• berkanozturk
In summary, the homework problem involves analyzing laminar flows in two parallel pipes of different diameters, connected to the same manifolds. The pressure drops across the pipes will be the same, but the flow rates will be different due to varying flow resistance. This can be compared to the electrical analog of two resistors in parallel. The Bernoulli equation can be used to analyze the pressure and velocity relationship, but the resulting equations will depend on the material properties and level of the pipes.
berkanozturk

## Homework Statement

Consider an apparatus design in which two tubes of different diameters are connected in parallel to each other.
The flow is steady and fully developd in both tubes. Do your analysis regarding
a)the governing differential equations for the case that in both tubes laminar flows occur.

## The Attempt at a Solution

Hello everyone,
For one pipe, we can simply use Reynolds transport theorem for a differential volume, and then get the related conservation of mass and momentum equations for 1 PIPE. However, when there are two pipes, how should I relate it? I could not solve it, hope you can help me. thanks for reading so far...

best regards
berkan

Assuming the pipes are connected to the same manifolds (headers), then the pressure drops across the pipes (lengthwise) would be the same. The flow rates would be different because the flow resistance would be different (including the cross-sectional areas).

The electrical analog is two resistors in parallel. Both resistors have the same potential drop across their terminals, but the current (charge flow rate) is different.

using bernoullli equation;

P/p + 1/2(V)^2=constant, (P:pressure, p:density, V:velocity)

lets say pipe1 is carrying the main stream and pipe2 and pipe3 are the parallel pipes with different diameters,

then it must be;

P1/p + 1/2(V1)^2 = P2/p + 1/2(V2)^2 = P3/p + 1/2(V3)^2

Remember;

Q=A*V

for different diameters crossectional area difference also changes V (as i know, correct me if i m wrong), so;

P2=P3 can not be achieved.

when it comes to may be

P1=P2 or P1=P3 ?

it depends on V1, V2 and V3 again. the same V will result the same P if material properties (heat, density etc.) and level of pipes not changed.

Last edited:

## 1. What is the concept of flow through parallel pipes with different diameters?

The concept of flow through parallel pipes with different diameters refers to the movement of a fluid through multiple pipes of varying sizes that are arranged in a parallel manner. This flow is driven by a pressure difference between the inlet and outlet of the pipes.

## 2. How does the diameter of a pipe affect the flow rate?

The diameter of a pipe has a direct impact on the flow rate. A larger diameter pipe allows for a greater volume of fluid to flow through, resulting in a higher flow rate. This is due to the fact that a larger pipe has a larger cross-sectional area, which reduces the frictional resistance to flow.

## 3. What is the equation for calculating flow rate through parallel pipes with different diameters?

The equation for calculating flow rate through parallel pipes with different diameters is Q = A1V1 = A2V2 = A3V3, where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the fluid.

## 4. How does the pressure difference between pipes affect the flow rate?

The pressure difference between pipes is the driving force for flow in this system. A greater pressure difference results in a higher flow rate, as it creates a larger driving force for the fluid to move through the pipes.

## 5. What factors can affect the flow rate through parallel pipes with different diameters?

Aside from pipe diameter and pressure difference, other factors that can affect the flow rate through parallel pipes with different diameters include the viscosity of the fluid, the length and roughness of the pipes, and any obstructions or bends in the pipe system.

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