The height of the water column (T=20 ºC) in the open tank is 4.5 m. Calculate the pressure acting on the bottom of the tank. Remember to count atmosphere pressure to the answer

To calculate the pressure at the bottom of the tank, we need to account for both the pressure due to the water column and atmospheric pressure. Here's how we can approach the problem step by step:

### Given:
- Height of the water column, \( h = 4.5 \, \text{m} \)
- Water temperature, \( T = 20^\circ \text{C} \)
- Gravitational acceleration, \( g = 9.81 \, \text{m/s}^2 \)
- Density of water at \( T = 20^\circ \text{C} \), \( \rho = 998 \, \text{kg/m}^3 \)
- Atmospheric pressure, \( P_{\text{atm}} = 101325 \, \text{Pa} \)

### Steps:

1. **Hydrostatic Pressure (due to the water column)**:
   \[
   P_{\text{water}} = \rho g h
   \]
   Substituting the values:
   \[
   P_{\text{water}} = 998 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 4.5 \, \text{m}
   \]
   \[
   P_{\text{water}} = 44047.29 \, \text{Pa}
   \]

2. **Total Pressure at the Bottom of the Tank**:
   The total pressure is the sum of the atmospheric pressure and the hydrostatic pressure from the water column:
   \[
   P_{\text{total}} = P_{\text{atm}} + P_{\text{water}}
   \]
   Substituting the values:
   \[
   P_{\text{total}} = 101325 \, \text{Pa} + 44047.29 \, \text{Pa}
   \]
   \[
   P_{\text{total}} = 145372.29 \, \text{Pa}
   \]

### Answer:
The total pressure acting on the bottom of the tank is **145,372 Pa** (or 145.37 kPa).

Would you like more details or have any questions? 

Here are some related questions to explore further:

1. How does the height of the water column affect the pressure at the bottom?
2. What would happen to the pressure if the tank were sealed instead of open to the atmosphere?
3. How does water temperature influence the density and thus the pressure?
4. What if the liquid in the tank were not water, but another substance like oil?
5. How would the pressure change if the tank were located at a higher altitude?

**Tip**: Always remember that atmospheric pressure is a significant part of total pressure in open systems!

The height of the water column (T=20 ºC) in the open tank is 4.5 m. Calculate the pressure acting on the bottom of the tank. Remember to count atmosphere pressure to the answer.

Learn how to calculate the total pressure at the bottom of a tank with a 4.5-meter water column (T=20°C), including atmospheric pressure. This problem involves fluid mechanics concepts, such as hydrostatic pressure and total pressure, and is ideal for students in Grades 10-12.

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