Solving Bernoulli's Principle Problem: Flow Rate in Horizontal Pipes

In summary, the speaker is struggling with a Bernoulli's principle problem involving a horizontal pipe with a diameter of 11.6 cm and a smooth reduction to a pipe with a diameter of 4.72 cm. They are unsure of which equation to use due to having two unknowns, v1 and v2, and are advised to use the equation of continuity, which states that the same amount of mass flows past each point.
  • #1
Cyrad2
13
0
Hi! This is the first question on my homework, so it's suppost to be the easiest, but I'm not sure how to tackle it. It's a Bernoulli's principle problem. Here it is:

A horizontal pipe 11.6 cm in diameter has a smooth reduction to a pipe 4.72 cm in diameter. If the pressure of the water in the larger pipe is 8.1E4 Pa and the 6.82E4 Pa pressure in the smaller pipe is at what rate does water flow through the pipes?

So I thought I'd use the equation:
P1 + .5pv1^2+pgy1 = P2 + .5pv2^2+pgy2

I'm not sure how to apply this to my problem because the equation has two unknowns: v1 and v2. Is there another bernoulli's equation i should be using?? There are several variations in my text, but none seem to work. Thanks, Brad
 
Physics news on Phys.org
  • #2
equation of continuity

Cyrad2 said:
I'm not sure how to apply this to my problem because the equation has two unknowns: v1 and v2. Is there another bernoulli's equation i should be using??
You need to apply the continuity equation, which says that the same amount of mass flows past each point. It can be written as [itex]A_1 v_1 = A_2 v_2[/itex], where A is the cross-sectional area.
 
  • #3


Hi Brad,

To solve this problem, you can use the continuity equation in addition to Bernoulli's principle. The continuity equation states that the flow rate (Q) is equal at any two points in a fluid system, so:

Q1 = Q2

Where Q1 is the flow rate in the larger pipe and Q2 is the flow rate in the smaller pipe.

Using this equation, we can set up a ratio between the two flow rates:

Q1/Q2 = A2/A1

Where A1 and A2 are the cross-sectional areas of the larger and smaller pipes, respectively.

We can rearrange this equation to solve for Q1:

Q1 = Q2 * (A1/A2)

Substituting in the values given in the problem, we get:

Q1 = Q2 * (11.6 cm/4.72 cm)^2

Now, we can use Bernoulli's principle to solve for the flow rate in the smaller pipe (Q2). Setting up the equation with the given pressures and using the fact that the pipes are horizontal (y1 = y2), we get:

8.1E4 Pa + 0.5pv1^2 = 6.82E4 Pa + 0.5pv2^2

Solving for v2, we get:

v2 = √(2*(8.1E4 Pa - 6.82E4 Pa)/p)

Where p is the density of water (1000 kg/m^3).

Now, we can plug this value into our equation for Q1:

Q1 = (1000 kg/m^3 * √(2*(8.1E4 Pa - 6.82E4 Pa)/1000 kg/m^3)) * (11.6 cm/4.72 cm)^2

Simplifying, we get:

Q1 = 0.14 m^3/s

So, the rate of flow in the larger pipe is 0.14 m^3/s. I hope this helps! Let me know if you have any further questions.
 

1. What is Bernoulli's Principle and how does it relate to flow rate in horizontal pipes?

Bernoulli's Principle states that in a fluid flow, an increase in the speed of the fluid will result in a decrease in pressure, and vice versa. In horizontal pipes, this principle can be applied to determine the relationship between flow rate, pipe diameter, and pressure.

2. What factors affect the flow rate in horizontal pipes?

The flow rate in horizontal pipes is affected by several factors such as the diameter of the pipe, the viscosity of the fluid, the length of the pipe, and the pressure difference between the two ends of the pipe.

3. How do you calculate the flow rate in horizontal pipes using Bernoulli's Principle?

The flow rate in horizontal pipes can be calculated using the equation: Q = (π * r^4 * ΔP) / (8 * η * L), where Q is the flow rate, r is the radius of the pipe, ΔP is the pressure difference between the two ends of the pipe, η is the viscosity of the fluid, and L is the length of the pipe.

4. Can Bernoulli's Principle be applied to all types of fluids in horizontal pipes?

Bernoulli's Principle can be applied to both ideal and real fluids in horizontal pipes, as long as the flow is steady and the fluid is incompressible.

5. How can Bernoulli's Principle be used to optimize flow rate in horizontal pipes?

By understanding the relationship between flow rate, pipe diameter, and pressure, Bernoulli's Principle can be used to optimize flow rate in horizontal pipes. This can be achieved by adjusting the diameter of the pipe, changing the pressure difference, or using a more viscous fluid, depending on the desired flow rate.

Similar threads

  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Replies
204
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
855
  • Aerospace Engineering
Replies
10
Views
600
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Mechanical Engineering
Replies
31
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Back
Top