Momentum and continuity equation

[andyb1990]

Homework Statement

Follow the link to see the question,

http://img507.imageshack.us/img507/2246/fluidquestion.png

Homework Equations

The Attempt at a Solution

currently I can't do part a) but from using part a) I can obtain the forces acting on the cone by using the first part of the equation (ρQ^2/2*A2) and then the force acting on the nozzle by using all of the equation,

for part a) I currently have used the continuity equation to work out what v1 and v2

v1= 0.764 m/s and v2= 8.475 m/s

then I am stuck as what to do with bernoulli's equation if that is the correct next step?

 

[berkeman]

Homework Statement

Follow the link to see the question,

http://img507.imageshack.us/img507/2246/fluidquestion.png

Homework Equations

The Attempt at a Solution

currently I can't do part a) but from using part a) I can obtain the forces acting on the cone by using the first part of the equation (ρQ^2/2*A2) and then the force acting on the nozzle by using all of the equation,

for part a) I currently have used the continuity equation to work out what v1 and v2

v1= 0.764 m/s and v2= 8.475 m/s

then I am stuck as what to do with bernoulli's equation if that is the correct next step?

Is this question from a take-home exam?

 

[andyb1990]

no, They are old exam questions to help us revise.

 

[LawrenceC]

Hint:

You have 3 equations to work with.

1. Continuity equation relates velocities to flow Q.
2. Bernoulli's equation relates velocities to pressure.
3. Momentum equation relates velocities to pressure force and bolt force.

Use all three and you will get the posted answer.

 

[rezeew]

Momentum and continuity equations are fundamental principles in fluid mechanics that govern the behavior of fluids in motion. The continuity equation states that the mass of a fluid remains constant within a closed system, meaning that the mass flow rate at any point in the system must be equal. This equation is based on the principle of conservation of mass and is essential in analyzing the flow of fluids in pipes, nozzles, and other systems.

The momentum equation, on the other hand, is based on the principle of conservation of momentum and states that the total momentum of a fluid remains constant within a closed system. This equation takes into account the forces acting on the fluid, such as pressure, gravity, and viscous forces, and is used to analyze the motion of fluids in different situations.

In the given question, the continuity equation can be used to determine the velocities at points 1 and 2, using the given mass flow rate and cross-sectional areas. Once these velocities are known, the momentum equation can be used to calculate the forces acting on the cone and the nozzle. This can be done by plugging in the known values for velocity, density, and area into the equation.

In terms of using Bernoulli's equation, this can be used to analyze the pressure changes in the fluid as it moves through the system. This equation takes into account the potential, kinetic, and pressure energies of the fluid and can be useful in understanding the behavior of the fluid at different points in the system.

Overall, the combination of the continuity and momentum equations, along with Bernoulli's equation, can provide a comprehensive analysis of the fluid flow in the given system. By using these principles, a scientist can gain a better understanding of the forces and pressures acting on the fluid and how it behaves as it moves through the system.