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 kg/m3.
3.9x10^5 N/m^2
To find the water pressure at ground level in the hose, we can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity acting on the fluid.
The formula to calculate hydrostatic pressure is:
P = ρgh
Where:
P = pressure
ρ = density of the fluid = 1000 kg/m³ (given)
g = acceleration due to gravity = 9.8 m/s²
h = height of the fluid column
In this case, the height of the fluid column is the difference in height between the bottom of the tank and ground level. We are given that the depth of water in the tank is 10 m, and the bottom of the tank is 20 m above ground. Therefore, the height of the fluid column is:
h = 10 m + 20 m = 30 m
Now, we can plug in the values into the formula to calculate the pressure at ground level:
P = (1000 kg/m³) * (9.8 m/s²) * (30 m) = 294,000 Pa
Therefore, the water pressure at ground level in the hose is closest to 294,000 Pa.