An aquarium 6 ft long, 4 ft wide, and 4 ft deep is full of water. (Recall that the weight density of water is 62.5 lb/ft^3.
(a) Find the hydrostatic pressure on the bottom of the aquarium.
(b) Find the hydrostatic force on the bottom of the aquarium.
(c) Find the hydrostatic force on one end of the aquarium.

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Answer:

Certainly! Let's calculate the values.

(a) Hydrostatic pressure on the bottom (\( P \)):

\[ P = 62.5 \, \text{lb/ft}^3 \cdot 32.2 \, \text{ft/s}^2 \cdot 4 \, \text{ft} \]

\[ P \approx 8000 \, \text{lb/ft}^2 \]

(b) Hydrostatic force on the bottom (\( F \)):

\[ F = P \cdot (6 \, \text{ft} \cdot 4 \, \text{ft}) \]

\[ F \approx 8000 \, \text{lb/ft}^2 \cdot 24 \, \text{ft}^2 \]

\[ F \approx 192,000 \, \text{lb} \]

(c) Hydrostatic force on one end (\( F' \)):

\[ F' = P \cdot (6 \, \text{ft} \cdot 4 \, \text{ft}) \]

\[ F' \approx 8000 \, \text{lb/ft}^2 \cdot 24 \, \text{ft}^2 \]

\[ F' \approx 192,000 \, \text{lb} \]

So, the hydrostatic pressure on the bottom is approximately \( 8000 \, \text{lb/ft}^2 \), and both the hydrostatic force on the bottom and on one end are approximately 192,000 lb.

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