Solving the Continuity Equation

• kinglk
In summary, Daniel is having trouble understanding how the continuity equation works and is looking for help with a problem on his assignment. Part 2 of the question asks him to use Bernoulli's equation to explain how it relates to continuity equation.
kinglk
i do not understand how the continuity equation works?

What continuity equation do you refer to?I can think of 2 or maybe more,but u need to be more specific.

Daniel.

that is the problem that i have ran into. on my assignment it does not say. it just ask us to use coninuity equation to explain how jet engines provide a forward thrust for an airplane? i have tried to research it but i am still lost.

part 2 of the question ask us to use Bernoulli's equation and explain hoe it relates to continuity equation?

This equation

$$\frac{\partial\rho\left(\vec{r},t\right)}{\partial t}+\nabla\cdot\left[\rho\left(\vec{r},t\right)\vec{v}\left(\vec{r},t\right)\right]= 0$$

Daniel.

kinglk said:
that is the problem that i have ran into. on my assignment it does not say. it just ask us to use coninuity equation to explain how jet engines provide a forward thrust for an airplane? i have tried to research it but i am still lost.

part 2 of the question ask us to use Bernoulli's equation and explain hoe it relates to continuity equation?

Hello, am study Continuity Equation right now for my problem Solving Class at ITT Tech
The Continuity Equation was give in the book. A1V1=A2V2 where A1 is the cross-sectional area at point 1, V1 is the velocity of the fluid at point 1, A2 is the cross-sectional area at point 2, and then V2 is the velocity of the fluid at point 2. Like you I stuck on Skill Level Problem II about using the equation to explain how jet engines provide forward trust for an airplane.

The Bernoulli's Equation and I still search for the equation but I think I end up using the one from Engineering Tool Box. The link is http://www.engineeringtoolbox.com/bernouilli-equation-d_183.html. I hope this helps but if you already finish maybe you can send help on the jet engine problem.

Last edited by a moderator:
kinglk said:
that is the problem that i have ran into. on my assignment it does not say. it just ask us to use coninuity equation to explain how jet engines provide a forward thrust for an airplane? i have tried to research it but i am still lost.

The equation of continuity in fluid dynamics is used when a fluid flows through an area which is then changed. The total flow remains constant i.e. volume per unit time is constant.

In equation form this is

A1v1=A2v2

How would A2 have to be with respect to A1 for there to be an increase in velocity?

kinglk said:
part 2 of the question ask us to use Bernoulli's equation and explain hoe it relates to continuity equation?

This ol' thread is locked. (And by "old", I mean that literally.)

1. What is the continuity equation?

The continuity equation is a mathematical representation of the principle of conservation of mass. It states that the rate of change of mass within a system is equal to the net flow of mass into or out of the system.

2. Why is the continuity equation important?

The continuity equation is important because it is a fundamental principle in many fields of science, including fluid mechanics, thermodynamics, and electromagnetism. It allows us to understand and predict the behavior of systems where mass is conserved.

3. How is the continuity equation solved?

The continuity equation can be solved by using the mathematical methods of calculus, specifically the concept of a derivative. The equation can be rearranged and solved for the unknown variable, such as velocity or density.

4. What are the assumptions made when solving the continuity equation?

The continuity equation assumes that the system is closed, meaning that there is no mass entering or leaving the system. It also assumes that the fluid is incompressible, meaning that its density remains constant. Additionally, it assumes that the flow is steady, meaning that the velocity does not change over time.

5. How is the continuity equation applied in real-world situations?

The continuity equation has many practical applications, such as predicting the flow of fluids in pipes, understanding the behavior of weather systems, and modeling the transport of contaminants in groundwater. It is also used in the design of various engineering systems, such as pumps and turbines.

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