The surface of water in a water tank on the top of a house is 4 m above the tap level. Find the pressure of water at the tap, when the tap is closed. Is it necessary to specify that the tap is closed? Take `g=10ms^-2`

Explanation

To solve the problem, we need to calculate the pressure of water at the tap level when the tap is closed. We can use the hydrostatic pressure formula for this purpose.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Height of the water column (h) = 4 m
- Acceleration due to gravity (g) = 10 m/s²
- Density of water (ρ) = 1000 kg/m³ (standard value)

2. **Understand the Pressure Formula:**
The pressure at a certain depth in a fluid is given by the formula:
\[ P = \rho g h \]
where:
- \( P \) = pressure at the depth
- \( \rho \) = density of the fluid (water in this case)
- \( g \) = acceleration due to gravity
- \( h \) = height of the fluid column above the point where pressure is being measured

3. **Substitute the Known Values:**
Now, substituting the values into the formula:
\[ P = 1000 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \times 4 \, \text{m} \]

4. **Calculate the Pressure:**
Performing the multiplication:
\[ P = 1000 \times 10 \times 4 = 40000 \, \text{N/m}^2 \]

5. **Final Answer:**
The pressure of water at the tap when the tap is closed is:
\[ P = 40000 \, \text{N/m}^2 \]

6. **Discuss the Importance of the Tap Being Closed:**
It is necessary to specify that the tap is closed because:
- When the tap is closed, the pressure at the tap is solely due to the height of the water column above it.
- If the tap were open, the pressure at the tap would not just be due to the height of the water column, as water would flow out and the water level in the tank would decrease, affecting the pressure.