Bernoulli Principe - Steps For Computing Curves (Algebra)

This animation uses the following steps to compute the velocity and pressure everywhere:

1. Assign an arbitrary pressure and an arbitrary velocity at the entrance point at the far left. This point will be referred to as point a below.
2. Since the water is incompressible, it must flow more quickly to "squeeze" through the narrow sections of the pipe. We can compute the velocity at any point by realizing that if the pipe narrows at point b to, say, one-third of its original height at point a, the fluid must travel three times faster. As part of this step, we select an arbitrary fluid density, and an arbitrary flow rate.

An engineer would compute the velocity values using the equation of continuity, and explain the constant flow rate by stating this fluid is steady state with no pooling.
3. We can compute the pressure at any point b using the Bernoulli Equation, given the pressure and velocity at point a, the fluid density, and the velocity at point b:
1. Ignore the two terms containing height since the average heights at a and b are the same so they cancel each other.
2. Plug in the pressure and velocity at point a, the fluid density, and the velocity at point b.
3. Solve for pressure at point b.