Question
A water tank is 5m tall. What is the pressure at the bottom of the tank? (Density =100kg/m^2 g= 9.8m/s^2)
Answers
GPT-4o mini
To determine the pressure at the bottom of a water tank, you can use the formula for hydrostatic pressure, which is given by:
\[
P = \rho g h
\]
where:
- \(P\) is the pressure at the depth,
- \(\rho\) is the density of the fluid (water in this case),
- \(g\) is the acceleration due to gravity,
- \(h\) is the height of the fluid column.
From the information given:
- \(\rho = 1000 \, \text{kg/m}^3\) (this is the typical density of water, not 100 kg/m² which seems to be a typo),
- \(g = 9.8 \, \text{m/s}^2\),
- \(h = 5 \, \text{m}\).
Now, substituting the values into the formula:
\[
P = 1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m}
\]
\[
P = 1000 \times 9.8 \times 5
\]
\[
P = 49000 \, \text{Pa}
\]
Thus, the pressure at the bottom of the tank is **49,000 Pascals** (Pa) or **49 kPa**.
\[
P = \rho g h
\]
where:
- \(P\) is the pressure at the depth,
- \(\rho\) is the density of the fluid (water in this case),
- \(g\) is the acceleration due to gravity,
- \(h\) is the height of the fluid column.
From the information given:
- \(\rho = 1000 \, \text{kg/m}^3\) (this is the typical density of water, not 100 kg/m² which seems to be a typo),
- \(g = 9.8 \, \text{m/s}^2\),
- \(h = 5 \, \text{m}\).
Now, substituting the values into the formula:
\[
P = 1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m}
\]
\[
P = 1000 \times 9.8 \times 5
\]
\[
P = 49000 \, \text{Pa}
\]
Thus, the pressure at the bottom of the tank is **49,000 Pascals** (Pa) or **49 kPa**.