# Help Understanding Volume Flow Rate / Bernoulli's

• KendrickLamar
In summary, the conversation discusses the concept of using volume flow rate in Bernoulli's equation and clarifies the relationship between A_2 and V_2. It also explains the concept of cross sectional area and how it relates to volumetric flow rate.

#### KendrickLamar

Hey guys, just have a question because I'm having a little trouble understanding like how exactly to use the volume flow rate with bernoulli's equation. (wasnt sure which section to put this in but is more of a concept question using homework examples)

Like the volume flow rate i understand A1v1=A2v2
for example i was doing this problem : https://www.physicsforums.com/showthread.php?t=80584

Well its inversely proportional right but (im just being stupid probably because I'm really tired) but if A2 is 1/4 the size of A1 for example, then v2 is going to be 4 x the size of V1? like

A1v1 = 1/4A2v2 so 4A1/v1 = A2v2 then v2 = 4(A1/A2)(v1), well like in the problem i linked, what happens to that A1/A2? why does it disappear when being plugged into bernoulli's equation?

Also another question is the A = cross sectional area right? what's that even mean like is that the same as surface area, or regular area, or what? because in a problem like this https://www.physicsforums.com/showthread.php?t=65810 (now I am not sure if the member solved it 100% correct) but the person here puts Volume Flow Rate = pir^2v1 for example, what is the volume flow rate in this case i don't understand and is A just the area of a circle on the tube , even tho its open its not used like a cylinder's area?

thanks if anyone can help me out I am like brain dead at the moment.

If $A_2$ is 1/4 $A_1$ then yes, $V_2$ will be 4 times $V_1$.

I'm not really sure what you mean when you say it "disappears?"

Cross sectional area is the area of a cross section. Say you have a piece of pipe. Stand the pipe on it's end on top of a piece of paper, then trace the inside of the pipe onto the paper. Find the area of that circle ($A=\pi r^2$) and that's the cross sectional area.

Volumetric flow rate is a volume per unit time (e.g., $\frac{m^3}{sec}$) If you do unit analysis you'll see that cross sectional area (e.g., $m^2$) times fluid velocity (e.g., $\frac{m}{sec}$) gives you volumetric flow rate.

## 1. What is volume flow rate and how is it measured?

Volume flow rate is the amount of fluid that flows through a specific point in a given amount of time. It is typically measured in units of volume per time, such as cubic meters per second. This can be calculated by dividing the volume of fluid that passes through the point by the time it takes to pass. It can also be measured using specialized instruments, such as flow meters.

## 2. How does Bernoulli's principle relate to fluid flow?

Bernoulli's principle states that as the speed of a fluid increases, its pressure decreases. This principle is important in understanding fluid flow because it explains the relationship between the speed and pressure of a fluid. As a fluid flows through a constricted area, such as a pipe, its speed increases and its pressure decreases. This principle is used in various applications, including the design of airplane wings and the functioning of carburetors.

## 3. What factors affect the volume flow rate of a fluid?

The volume flow rate of a fluid can be affected by several factors, including the pressure difference between two points, the viscosity of the fluid, the density of the fluid, and the size and shape of the conduit through which the fluid is flowing. Changes in any of these factors can impact the volume flow rate of a fluid.

## 4. How can the volume flow rate be increased?

The volume flow rate can be increased by increasing the pressure difference between two points, decreasing the viscosity of the fluid, increasing the density of the fluid, and using a larger or smoother conduit for the fluid to flow through. Additionally, the volume flow rate can be increased by using techniques such as laminar flow or turbulence control.

## 5. What are some real-life applications of understanding volume flow rate and Bernoulli's principle?

Understanding volume flow rate and Bernoulli's principle is important in various fields, including fluid mechanics, aerodynamics, and engineering. It is used in the design and functioning of airplanes, cars, and other vehicles. It is also applied in industries such as oil and gas, where the flow rate of fluids through pipelines is critical. Additionally, understanding these concepts can help in the design and optimization of pumps, valves, and other fluid systems.