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Velocity and Pressure in Flow Net
Velocity and pressure are two important parameters in a flow net. In a flow net, the velocity in the stream tube is directly proportional to the mesh size. The pressure difference between any two meshes can be determined by the application of the Bernoulli equation. However, the velocity at a boundary surface is always zero.
Velocity and Mesh Size
The velocity in a flow net is directly proportional to the mesh size. The streamlines in a flow net are drawn such that they are parallel to the direction of flow. The streamlines are spaced closer together in regions of high velocity and farther apart in regions of low velocity. The streamlines form a pattern that looks like a net, hence the name flow net.
Pressure and Bernoulli Equation
The Bernoulli equation relates the pressure, velocity, and elevation of a fluid flowing in a pipe or channel. The equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid is constant along a streamline. Therefore, the pressure difference between any two meshes can be determined by the application of the Bernoulli equation.
Velocity Potential
The velocity potential is a scalar function that describes the flow of a fluid. It is defined as the work that must be done per unit mass to move a fluid element from a reference point to a given point in the flow field. The velocity potential increases in the downstream direction, as the fluid flows from a region of high pressure to a region of low pressure.
Conclusion
In conclusion, the pressure difference between any two meshes can be determined by the application of the Bernoulli equation in a flow net. The velocity in the stream tube is directly proportional to the mesh size, and the velocity at a boundary surface is always zero. The velocity potential increases in the downstream direction, as the fluid flows from a region of high pressure to a region of low pressure.