linean

(Headbang)Section project: Tidal power plants use "tidal energy" to produce electrical energy. To construct a tidal power plant, a dam is built to seperate a bay from the sea. Electrical energy is produced as the water flows back and forth between the bay and the sea. The amount of natural energy produced depends on the volume of the basin and the tidal range - the vertical distance between high and low tides.9 throughout the world. several natural bays have tidal ranges in excess of 15 feet; the Bay of Fundy in Nova Scotia has a tidal range of 47.5 feet).
a) consider a bay with a rectangular base( as shown in picture pg 453 calculus..sory i can's post this pic.) THe bay has a tidal range of 25 feet, with low tide corresponding to y =0. How much water does the bay hold at high tide?
b) the amount of enery produce during the filling(or emptying) of the bay is proportional to the amount of work required to the fill(or empty) the bay. How much work is required to fill the bay with seawater? (Use seawater with density of 64 pounds oer cubic foot)

HallsofIvy

MHF Helper
(Headbang)Section project: Tidal power plants use "tidal energy" to produce electrical energy. To construct a tidal power plant, a dam is built to seperate a bay from the sea. Electrical energy is produced as the water flows back and forth between the bay and the sea. The amount of natural energy produced depends on the volume of the basin and the tidal range - the vertical distance between high and low tides.9 throughout the world. several natural bays have tidal ranges in excess of 15 feet; the Bay of Fundy in Nova Scotia has a tidal range of 47.5 feet).
a) consider a bay with a rectangular base( as shown in picture pg 453 calculus..sory i can's post this pic.) THe bay has a tidal range of 25 feet, with low tide corresponding to y =0. How much water does the bay hold at high tide?
We don't need a picture but we do need to know the length and width of the bay! Those are probably given in the picture.

b) the amount of enery produce during the filling(or emptying) of the bay is proportional to the amount of work required to the fill(or empty) the bay. How much work is required to fill the bay with seawater? (Use seawater with density of 64 pounds oer cubic foot)
In order to "empty" the bay, we must raise all the water to the height of its top- 25 feet. Imagine a "layer" of water at height x above the base level, 0. It must be raised 25- x feet. It contains LWdx cubic feet where L is the length of the bay, W is the width of the bay, and dx represents the "thickness" of the layer. That layer has weight 64LWdx so 64LW(25- x)dx is the work done lifting that layer 25- x feet to go out of or into the bay. Integrate over all layers of water: $$\displaystyle 64LW \int_0^{25}(25- x)dx$$.