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# A 1-m-tall barrel is closed on top except for a thin pipe extending $5 \mathrm{~m}$ up from the top. When the barrel is filled with water up to the base of the pipe (1 meter deep), the water pressure on the bottom of the barrel is $10 \mathrm{kPa}$. What is the pressure on the bottom when water is added to fill the pipe to its top?

Solution

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$\textbf{Given}$

$h_1= 1 \text{ m}$

$h_2= 6 \text{ m}$

$p_1 = 10 \text{ kPa}$

$\textbf{Approach}$

The water pressure can be calculated using the following equation:

$p = \rho \cdot g \cdot h$

$\textbf{Solution}$

Inserting numerical values into the equation we get that the pressure is:

$p_2 = 1000$ $\dfrac{\text{kg}}{\text{m}^3} \cdot 10$ $\dfrac{\text{m}}{ \text{s}^2} \cdot 6 \text{ m} = 60000 \text{ Pa}$

$\boxed {p_2 = 60 \text{ kPa}}$

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