What are similarities between bernoulli's principle and pascal's law?

Answer 1

Bernoulli's Principle uses Pascal's Law to relate the final and initial states of an ideal liquid.

Pascal's Law says that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid, meaning that for an ideal fluid (Δρ = 0):

ΔP = ρgΔh

where ρ is fluid density, g is gravitational pull and h is height pf fluid above measurement.

Bernoulli's Principle states that for an ideal fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy:

0.5ρv2 +ρgh + P = constant

Where v = velocity of the fluid. If the fluid is stationary, v = 0. Taking the derivative of this:

Δ(ρgh) + ΔP = 0

Again, assuming ideality,

ρgΔh + ΔP = 0

If we raise the fluid, the pressure will drop, meaning that we can rearrange the equation to:

ΔP = ρgΔh