Final answer:
The gauge pressure on the bottom of the tank can be calculated using the formula P = ρgh, where P is the gauge pressure, ρ is the density of the water, g is the acceleration due to gravity, and h is the height of the water. The gauge pressure on the bottom of the tank is 6370 Pa.
Step-by-step explanation:
The gauge pressure on the bottom of the tank can be calculated using the formula P = ρgh, where P is the gauge pressure, ρ is the density of the water, g is the acceleration due to gravity, and h is the height of the water.
First, we need to convert the dimensions of the tank from meters to centimeters, since the density of water is usually given in g/cm³. The tank measures 75 cm x 50 cm, so the area of the bottom is (75 cm) x (50 cm) = 3750 cm². The height of the water is 65 cm. The density of water is approximately 1 g/cm³. The acceleration due to gravity is 9.8 m/s².
Now we can calculate the gauge pressure:
P = (1 g/cm³) x (9.8 m/s²) x (65 cm) = 6370 Pa
Therefore, the gauge pressure on the bottom of the tank is 6370 Pa.
To calculate the gauge pressure on the bottom of the rectangular fish tank, we can use the formula for pressure due to the weight of a liquid:
P = ρ * g * h
Where ρ (rho) is the density of water, g is the acceleration due to gravity, and h is the height of the water column.
The density of water (ρ) is typically 1000 kg/m³, and the standard acceleration due to gravity (g) is 9.8 m/s². The height (h) of the water column is given as 65 cm, which is 0.65 m.
Substituting the values:
P = (1000 kg/m³) * (9.8 m/s²) * (0.65 m)
P = 6370 Pa
So, the gauge pressure on the bottom of the tank is 6370 Pascal (Pa).