# How to Determine Flow Rate in a Pipe Using Fluid Dynamics?

• lurifax1
In summary, the conversation discusses the difficulty in using Bernoulli's equation to find the flowrate through a pipe with the same diameter on both ends. The equations for Bernoulli's principle and the Hagen-Poiseuille equation are mentioned, but it is noted that the latter does not take into account the height of the pipe. The individual also asks for assistance with their homework.
lurifax1

## Homework Statement

http://imgur.com/DSBFIeO
I want to find the flowrate through this pipe based on the pipe's diameter, height of the pipe and the pressure difference. I tried to use Bernoulli, but since the diameter on either end is the same, the terms cancel out. I guess Bernoulli's equation doesn't apply in this example

## Homework Equations

https://en.wikipedia.org/wiki/Bernoulli's_principle
https://en.wikipedia.org/wiki/Hagen–Poiseuille_equation

## The Attempt at a Solution

$P_1 + \rho g h_1 + \dfrac{1}{2}\rho {v_1}^2 = P_2+ \rho g h_2 + \dfrac{1}{2}\rho {v_2}^2 \\ {v_2}^2-{v_1}^2 = \dfrac{|P1-P2|-\rho g h_2}{0.5\rho}\\[2mm]$
I also looked at Poiseuille's equation: $\dfrac{\Delta V}{\Delta t}=\dfrac{\pi r^4 (P_1-P_2)}{8\eta l},\\[2mm]$
but this does not take the height of the pipe into effect.

man the forums are dead now could you please take a look at my homework?

## 1. What is fluid dynamics?

Fluid dynamics is the study of how fluids (liquids and gases) move and interact with their surroundings. It involves understanding the forces and motions that cause fluids to flow, as well as the properties of fluids such as viscosity and density.

## 2. What is a pipe?

A pipe is a hollow cylindrical structure that is used to transport fluids from one place to another. It can be made of various materials such as metal, plastic, or concrete, and is typically used for water, gas, or oil distribution.

## 3. How does fluid flow through a pipe?

Fluid flows through a pipe due to a pressure difference between the two ends. The fluid moves from an area of high pressure to an area of low pressure, and this creates a flow. The rate of flow depends on the pressure difference, the properties of the fluid, and the geometry of the pipe.

## 4. What factors affect fluid flow through a pipe?

The factors that affect fluid flow through a pipe include the pressure difference, the viscosity of the fluid, the diameter and length of the pipe, and the roughness of the pipe walls. Other factors such as temperature and the presence of obstacles or bends in the pipe can also impact the flow.

## 5. How is fluid flow in a pipe measured?

Fluid flow in a pipe is typically measured using a flow meter, which is a device that measures the rate of flow of a fluid. Different types of flow meters include ultrasonic, magnetic, and turbine meters, and they work by detecting the movement of the fluid through the pipe and converting it into a measurable value.

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