A rectangular fish tank measuring 0.80m × 0.55m is filled with water to a height of 61cm .
Part A
What is the gauge pressure on the bottom of the tank?
p = ρgh = 1000•9.8•0.61= 5978 N/m²
To find the gauge pressure on the bottom of the tank, we can use the formula for pressure:
Pressure = ρgh
where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
First, let's convert the dimensions of the tank to meters:
Length = 0.80 m
Width = 0.55 m
Height of the water column = 61 cm = 0.61 m
Next, let's find the density of water. The density of water is approximately 1000 kg/m³.
Now, we can calculate the gauge pressure:
Pressure = (density of water) * (acceleration due to gravity) * (height of water column)
= (1000 kg/m³) * (9.8 m/s²) * (0.61 m)
Calculating the value, we get:
Pressure ≈ 5969 Pa (rounded to the nearest whole number)
So, the gauge pressure on the bottom of the tank is approximately 5969 Pa.
To determine the gauge pressure on the bottom of the tank, we first need to understand the concept of gauge pressure.
Gauge pressure is the pressure measured relative to atmospheric pressure. It is calculated by subtracting atmospheric pressure from the total pressure exerted on a surface.
In this case, the fish tank is filled with water, which exerts a pressure on the bottom of the tank due to its weight. The gauge pressure can be calculated using the equation:
Gauge Pressure = Total Pressure - Atmospheric Pressure
Before we can calculate the gauge pressure, we need to find the total pressure and atmospheric pressure.
1. Total Pressure:
The total pressure exerted by water is calculated using the equation:
Total Pressure = Density × Gravity × Height
In this case, the density of water (ρ) is approximately 1000 kg/m^3 and gravity (g) is approximately 9.8 m/s^2. The height (h) is given as 61 cm, but we need to convert it to meters by dividing by 100:
Height (h) = 61 cm ÷ 100 = 0.61 m
So, the total pressure can be calculated as:
Total Pressure = 1000 kg/m^3 × 9.8 m/s^2 × 0.61 m = 5998 N/m^2 or Pascal (Pa)
2. Atmospheric Pressure:
The atmospheric pressure depends on the location and weather conditions. Standard atmospheric pressure at sea level is approximately 101325 Pa or 101.325 kPa.
Now that we have the total pressure and atmospheric pressure, we can calculate the gauge pressure:
Gauge Pressure = Total Pressure - Atmospheric Pressure
= 5998 Pa - 101325 Pa (or 101.325 kPa)
Calculate the difference to find the gauge pressure. Remember to use the appropriate units for the calculation.
So, the gauge pressure on the bottom of the tank can be calculated by simply subtracting the atmospheric pressure from the total pressure.