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Chapter 7: Problem 35

Develop the Froude number by starting with estimates of the fluid kinetic energy and fluid potential energy.

Short Answer

Expert verified
The Froude number is developed starting with estimates of the fluid kinetic energy and fluid potential energy as \(Fr = \sqrt{E_K / E_P}\) where \(E_K = 0.5 * d * A * v^2\) is the kinetic energy and \(E_P= d * g * h * A\) is the potential energy. Density is \(\d\), velocity is \(v\), height is \(h\), gravity is \(g\) and area is \(A\).

Step by step solution

01

Define and Calculate Kinetic Energy

The kinetic energy of a fluid is defined as \(E_K = 0.5 * d * A * v^2\) where \(d\) is the density of the fluid, \(A\) is the area through which the fluid is flowing and \(v\) is the velocity of the fluid.
02

Define and Calculate Potential Energy

The potential energy of a fluid is defined as \(E_P= d * g * h * A\) where \(d\) is the density of the fluid, \(g\) is the acceleration due to gravity, \(h\) is the height difference and \(A\) is the area through which the fluid is flowing.
03

Develop the Froude number

The Froude number is the ratio of the kinetic energy to the potential energy. It can be calculated as \(Fr = \sqrt{E_K / E_P}\) where \(E_K\) is the kinetic energy and \(E_P\) is the potential energy. If numbers were given for the density, velocity, height, gravity and area, these could be plugged in to get a numerical value for the Froude number. Otherwise we keep the formula to show how the Froude number is developed from estimates of fluid kinetic and potential energy.

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Most popular questions from this chapter

A mixing basin in a sewage filtration plant is stirred by a mechanical agitator with a power input \(\dot{W} \doteq F \cdot L / T\). Other parameters describing the performance of the mixing process are the fluid absolute viscosity \(\mu \doteq F \cdot T / L^{2},\) the basin volume \(V \doteq L^{3}\) and the velocity gradient \(G \doteq 1 / T\). Determine the form of the dimensionless relationship.

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