Note: Look at several versions of this problem.
Bernoulli's Law follows from the Conservation of Energy. Recall that Conservation of Energy says that if some form of energy increases, it is at the expense of some other form of energy, or of work done by the object. For example, if Kinetic Energy increases, either work must be done to cause the increase or potential energy must decrease. The sum of kinetic and potential energy changes and the work done by the object must equal zero (e.g., work done by an object is typically associated with negative changes in KE and PE).
Bernoulli's Law says that the sum of the quantities
.5 `rho v^2, where `rho is the Greek letter usually used to stand for density. This term is much like a kinetic energy term, and
`rho g h , which is much like a potential energy term, and
P, which is much like work done by an object,
is always the same in a flowing fluid, provided there are no dissipative energy losses.
The variables are v, h and P, which represent the fluid velocity, the fluid height, and the pressure; d is the density of the fluid, which will in this problem be assumed constant, and g is the acceleration of gravity.
If P remains the same and v increases, P+.5 `rho v^2 will increase. If .5 `rho v^2 + `rho g h + P is gonna remain the same, it's clear that `rho g h , and therefore h, must decrease.
If v remains the same and h increases, .5 `rho v^2+`rho g h will increase. If .5 `rho v^2 + `rho g h + P is gonna remain the same, it's clear that P must decrease.
If P remains the same and h increases, P+`rho g h will increase. If .5 `rho v^2 + `rho g h + P is gonna remain the same, it's clear that .5 `rho v^2, and therefore v, must decrease.
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