Then in a time \(\Delta t\), a volume \(v_{1} \Delta t A_{1}\) of fluid passes a fixed on that pipe. Therefore the fluid velocity in the new pipe must change to a new velocity \(v_{2}\) that satisfies...Then in a time \(\Delta t\), a volume \(v_{1} \Delta t A_{1}\) of fluid passes a fixed on that pipe. Therefore the fluid velocity in the new pipe must change to a new velocity \(v_{2}\) that satisfies \(v_{1} \Delta t A_{1}=v_{2} \Delta t A_{2}\), or \(v_{1} A_{1}=v_{2} A_{2}\). Water flows out of the hose relatively slowly; but if you place your thumb over the opening to block most of the flow, then water squirts out of the small remaining opening at high velocity.
Experimentally, we find that if you increase the pressure by some given amount at one location in a fluid, the pressure increases by that same amount everywhere in the fluid. This experimental result ...Experimentally, we find that if you increase the pressure by some given amount at one location in a fluid, the pressure increases by that same amount everywhere in the fluid. This experimental result is known as Pascal’s Principle.
