A water tank is filled to a depth of 10 m, and the bottom of the tank is 20 m above ground. A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The water pressure at ground level in the hose is closest to which of the following values? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
A) $2.0 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
B) $3.9 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
C) $9.2 \mathrm {~N} / \mathrm { m } ^ { 2 }$
D) The question cannot be answered because the cross sectional area of the tank is needed.

Question

A water tank is filled to a depth of  10 m, and the bottom of the tank is  20 m above ground. A water-filled hose that is  2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The water pressure at ground level in the hose is closest to which of the following values? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
A) $2.0 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
B) $3.9 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
C) $9.2 \mathrm {~N} / \mathrm { m } ^ { 2 }$
D) The question cannot be answered because the cross sectional area of the tank is needed.

Quizplus · Accepted Answer

The water pressure at ground level can be calculated using the equation $P = \rho gh$, where $\rho$ is the density of water ($1000 \, \mathrm{kg/m^3}$), $g$ is the acceleration due to gravity ($9.8 \, \mathrm{m/s^2}$), and $h$ is the total height of the water column above the point where the pressure is being measured ($10 \, \mathrm{m} + 20 \, \mathrm{m} = 30 \, \mathrm{m}$). Plugging in these values gives $P = 1000 \times 9.8 \times 30 = 294,000 \, \mathrm{N/m^2}$ or $2.94 \times 10^5 \, \mathrm{N/m^2}$, which is closest to choice B, $3.9 \times 10^5 \, \mathrm{N/m^2}$. The diameter of the hose is not needed to calculate the pressure at ground level.

A Water Tank Is Filled to a Depth of 1000 kg/m31000 \mathrm {~kg} / \mathrm { m } ^ { 3 }1000 kg/m3

A Water Tank Is Filled to a Depth of $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$