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An aquarium 5 ft long, 2 ft wide, and 3 ft deep is full of water. Find (a) the hydrostatic pressure on the bottom of the aquarium, (b) the hydrostatic force on the bottom, and (c) the hydrostatic force on one end of the aquarium.

For (a) the hydrostatic pressure is [tex] P = \rho gd [/tex] which is [tex]187.5 \frac{lb}{ft^{3}} [/tex].

For (b), the hydrostatic force is [tex] F = PA = (187.5 \frac{lb}{ft^{3}})(10 ft) = 1870\frac{lb}{ft^{2}} [/tex]

Now for (c), this is where I become stuck. I know that [tex] P = 62.5(x_{i}) [/tex]. So the water is pushing against the bottom of the aquarium, which is a rectangle. I took a partition of that side, and found the area to be [tex] 5P(\Delta x) = (5\Delta X)62.5x_{i} [/tex]. But I saw the answer, and they have that the area of the partition is [tex] 2\Delta x [/tex]. This in turn messes up the calculation of the integral. What am I doing wrong?

P.S: What exactly does this mean: we choose [tex] x_{i}\in [x_{i-1} , x_{i}] [/tex]? What does [tex] x_{i} [/tex] represent?

Thanks

For (a) the hydrostatic pressure is [tex] P = \rho gd [/tex] which is [tex]187.5 \frac{lb}{ft^{3}} [/tex].

For (b), the hydrostatic force is [tex] F = PA = (187.5 \frac{lb}{ft^{3}})(10 ft) = 1870\frac{lb}{ft^{2}} [/tex]

Now for (c), this is where I become stuck. I know that [tex] P = 62.5(x_{i}) [/tex]. So the water is pushing against the bottom of the aquarium, which is a rectangle. I took a partition of that side, and found the area to be [tex] 5P(\Delta x) = (5\Delta X)62.5x_{i} [/tex]. But I saw the answer, and they have that the area of the partition is [tex] 2\Delta x [/tex]. This in turn messes up the calculation of the integral. What am I doing wrong?

P.S: What exactly does this mean: we choose [tex] x_{i}\in [x_{i-1} , x_{i}] [/tex]? What does [tex] x_{i} [/tex] represent?

Thanks

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