Worksheet for Exploration $15\mathrm{.}2$: Bernoulli$$s Equation Bernoulli$$s equation describes the conservation of energy in an ideal fluid system. Assume an ideal fluid $($position is given in meters and pressure is given in pascals$).$ The dark blue in the animation is a section of water as it flows into the region marked by the horizontal line and the corresponding water that must move out of the region in the top right. We will explore the connection between Bernoulli's equation and conservation of energy. Restart $.$ Note: The format of the pressure is written in short hand. For example, atmospheric pressure, $1\mathrm{.}01$ x $105$ Pa$,$ is written as $1\mathrm{.}01$e$+005.$ The relationship between the speed and dimensions of the water going in compared with the water leaving is governed by the continuity equation $($what flows in must flow out unless there is a leak in the pipes!$)$: Av $=$ constant, where A is the cross$-$sectional area and v is the speed of the liquid. Assume the pipes are cylindrical. a$.$ b$.$ c$.$ What is the volume of both $($darker$)$ blue regions $($should be the same$)?$ Vleft$=\_\_\_\_\_\_\_$ Vright$=\_\_\_\_\_\_\_$ What is the speed of the water in the left pipe? Speed left$=\_\_\_\_\_\_\_$ What is the cross$-$sectional area of the left pipe? Aleft$=\_\_\_\_\_\_\_$