Chemical Engineering Help With Pressure And Velocity Relation
5.5 Pressure And Velocity Relation
In most of liquids and of gases, the mass density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. For this reason the fluid in such flows can be considered to be incompressible and these flows can be described as incompressible flow thus cab be explained by Bernoulli equations as Bernoulli performed his experiments on liquids and his equation in its original form is valid only for incompressible flow.
The original form of Bernoulli's equation valid at any point along a streamline is:
v2/2 + Ψ + p/ρ = constant
v = fluid flow speed at a point on a streamline,
Ψ = gravitational potential,
p = pressure at the point, and
ρ = density of the fluid at all points in the fluid.
The following assumptions must be met for the equation to apply:
1. The fluid must be incompressible thus even though pressure varies, the density must remain constant.
2. Bernoulli's equation is not applicable where there are acting viscous forces.
If the acceleration due to gravity (g) does not change over the length scale of the problem then Ψ=gz, where z is the elevation of the point above some reference plane (positive z-direction points upward, in the opposite direction to the gravitational acceleration).
By multiplying with the mass density ρ, the above equation can be rewritten as:
ρv2/2 + ρgz + p= constant
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