Differentiating the Integral Form of the Continuity Equation for Fluids

In summary, the conversation was about using the integral form of the continuity equation for a steady flow and showing that it can equal a given equation by taking its derivative. The homework equation involves velocity and density, and the question was about finding the derivative with respect to what variable. The attempted solution was to simplify the equation to rVA=0, but the person was unsure how to differentiate it to match the given equation. However, they realized that they had forgotten the chain rule from calculus and were overthinking the problem.
  • #1
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Homework Statement



I am working on a problem that asks to use the integral form of the continuity equation (for a steady flow) and show that it can equal this (by taking the derivative of it): dr/r + dV/V + dA/A = 0 where V is Velocity and r is the density.

Homework Equations



What would the derivative be with respect to?

The Attempt at a Solution



I was able to bring it down to: rVA=0 but I am unaware how to differentiate this so that it looks like the equation above.

Thanks.
 
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  • #2
Never mind... I have forgotten the old chain rule from calculus. I was over thinking this problem.
 

Related to Differentiating the Integral Form of the Continuity Equation for Fluids

1. What is the continuity equation for fluids?

The continuity equation for fluids is a fundamental equation in fluid mechanics that states that the rate of mass entering a system must be equal to the rate of mass leaving the system. In other words, the total mass of a fluid within a closed system must remain constant over time.

2. What is the integral form of the continuity equation for fluids?

The integral form of the continuity equation for fluids is a mathematical representation of the continuity equation that involves integrating the equation over a defined volume. This form is useful for analyzing the behavior of fluids within a specified region.

3. How is the integral form of the continuity equation derived?

The integral form of the continuity equation can be derived using the principles of conservation of mass and the divergence theorem. By applying these principles and simplifying the resulting equations, the integral form of the continuity equation can be obtained.

4. What is the significance of the integral form of the continuity equation in fluid dynamics?

The integral form of the continuity equation is significant in fluid dynamics because it allows for the analysis of fluid flow within a specified region. This form can be used to determine the velocity, flow rate, and other important parameters of a fluid within a given volume.

5. How is the integral form of the continuity equation differentiated?

The integral form of the continuity equation can be differentiated using the principles of calculus. By taking the partial derivatives of the equation with respect to time and spatial coordinates, the equation can be further analyzed to gain insights into the behavior of fluids within a system.

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