Calculating Pressure in a Liquid Flashcards

All 7 cards in this deck

What is the equation for the pressure due to a column of liquid?

$P = h \times \rho \times g$ — pressure = height (depth) of column $\times$ density $\times$ gravitational field strength.

State the units of each quantity in $P = h \rho g$.

$P$ in Pa, $h$ in m, $\rho$ in kg/m$^3$, $g$ in N/kg.

What are the steps to calculate the pressure due to a column of liquid?

e.g. water of density $1000$ kg/m$^3$ at a depth of $3$ m, $g = 10$ N/kg

1. Select $P = h\rho g$
2. Substitute: $P = 3 \times 1000 \times 10$
3. Pressure $= 30\,000$ Pa

What are the steps to find the depth $h$ from a pressure due to a liquid?

e.g. $P = 20\,000$ Pa in water, $\rho = 1000$ kg/m$^3$, $g = 10$ N/kg

1. Write $P = h\rho g$ and substitute: $20\,000 = h \times 1000 \times 10$
2. Rearrange: $h = \dfrac{20\,000}{1000 \times 10}$
3. $h = 2$ m

What are the steps to find the difference in pressure between two depths in a liquid?

e.g. between $2$ m and $5$ m deep in water ($\rho = 1000$ kg/m$^3$, $g = 10$ N/kg)

1. Find the difference in depth: $5 - 2 = 3$ m
2. Use $\Delta P = \Delta h \times \rho \times g = 3 \times 1000 \times 10$
3. Difference in pressure $= 30\,000$ Pa

True or false? In $P = h\rho g$, $h$ is the total height of the container.

False. $h$ is the depth of the point below the surface of the liquid.

Does $P = h\rho g$ give the total pressure at a depth in an open tank?

No — it gives only the pressure due to the liquid; add atmospheric pressure for the total.