Fluid flow problem with the momentum balance equation

Thread starter abstracted6
Start date Sep 20, 2012
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Balance Flow Fluid Fluid flow Momentum Momentum balance

In summary, the momentum balance equation is a fundamental equation in fluid mechanics that relates the forces acting on a fluid to its resulting motion. It is essential for analyzing fluid flow problems and allows for the prediction of flow behavior. Steady and unsteady fluid flow have different properties, and boundary conditions play a crucial role in solving the momentum balance equation. The equation can be simplified for specific types of fluid flow, but for more complex problems, the full equation must be used.

Sep 20, 2012

abstracted6

All problem info, and my work is done in the attached pdf.

Basically, I'm not sure that I have done it correctly.

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Sep 21, 2012

LawrenceC

What is the formula for the area of a circle in terms of diameter?

Sep 21, 2012

abstracted6

Ooops

So the answer is then:

F_p = -[itex]\rho[/itex]v_j²[itex]\frac{\pi}{4}[/itex](D₁² - D₂²)

Sep 21, 2012

LawrenceC

Looks good to me.

Sep 21, 2012

rude man

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Comment: interesting problem; case where change in momentum is vΔm instead of the usual mΔv.

What is the momentum balance equation?

The momentum balance equation is a fundamental equation of fluid mechanics that describes the relationship between the forces acting on a fluid and its resulting motion. It states that the rate of change of momentum of a fluid element is equal to the sum of all external forces acting on the element, including pressure, viscous forces, and body forces.

How does the momentum balance equation relate to fluid flow problems?

The momentum balance equation is essential for analyzing and understanding fluid flow problems. It allows us to determine the forces that affect the motion of a fluid and how they contribute to the overall flow behavior. By solving the momentum balance equation, we can predict the velocity and pressure distribution of a fluid in a given system.

What is the difference between steady and unsteady fluid flow?

Steady fluid flow refers to a situation where the fluid properties and flow behavior do not change over time. This means that the velocity, pressure, and other flow variables remain constant at any given point in the system. In contrast, unsteady fluid flow is characterized by a time-varying flow behavior, where the fluid properties and flow variables change with time.

How do boundary conditions affect the solution of the momentum balance equation?

Boundary conditions play a crucial role in solving the momentum balance equation. They specify the conditions at the boundaries of a system, such as the velocity or pressure, and help determine the unknown flow variables. Without proper boundary conditions, it is impossible to obtain a unique solution to the momentum balance equation.

Can the momentum balance equation be simplified for specific types of fluid flow?

Yes, the momentum balance equation can be simplified for different types of fluid flow, such as incompressible, inviscid, or laminar flow. In these cases, certain forces, such as viscosity or body forces, may be neglected, making the equation easier to solve. However, for more complex fluid flow problems, the full momentum balance equation must be used to accurately describe the flow behavior.