Final answer:
The gauge pressure on the bottom of a rectangular fish tank filled with water up to a height of 65 cm is calculated using the formula P = ρgh, resulting in a pressure of 6370 Pascals (Pa).
Step-by-step explanation:
To calculate the gauge pressure on the bottom of a tank, you can use the formula for pressure due to the weight of a liquid, which is P = ρgh, where ρ is the density of the liquid (in kg/m³), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the liquid column above the point of measurement (in meters).
In this case, the fish tank is filled with water (density of water = 1000 kg/m³) up to a height of 0.65 meters since 65 cm = 0.65 m. The gauge pressure at the bottom is the hydrostatic pressure due to the water above it, ignoring atmospheric pressure.
Using the values:
- Density of water, ρ = 1000 kg/m³
- Gravitational acceleration, g = 9.8 m/s³
- Height of water column, h = 0.65 m
The gauge pressure, P, can be calculated as follows:
P = ρgh
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 Pascals (Pa).