Final answer:
The pressure at a closed faucet on the second floor, 5 meters above the entry point, is 17.89 psi, after accounting for the loss in pressure due to the increase in height.
Step-by-step explanation:
To calculate the pressure at a closed faucet on the second floor, we need to consider the pressure at the entry point and the increase in height. The pressure due to height change can be calculated using the hydrostatic pressure equation. The hydrostatic pressure difference (ΔP) due to the elevation change is ΔP = ρgh, where ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²), and h is the height difference (5 m).
First, we convert the water's entry pressure from psi to pascals because the standard unit of pressure in physics is the pascal (Pa). Since 1 psi is approximately 6894.76 pascals,
Pressure at entry in Pa = 25 psi * 6894.76 Pa/psi = 172369 Pa
Now, calculate the hydrostatic pressure change:
ΔP = 1000 kg/m³ * 9.81 m/s² * 5 m
ΔP = 49050 Pa
The pressure decrease due to the 5-meter increase in height is 49050 Pa. To find the pressure at the closed faucet, we subtract this from the entry pressure:
Pressure at faucet in Pa = Pressure at entry in Pa - ΔP
Pressure at faucet in Pa = 172369 Pa - 49050 Pa
Pressure at faucet in Pa = 123319 Pa
Finally, we convert this pressure back to psi:
Pressure at faucet in psi = Pressure at faucet in Pa / 6894.76 Pa/psi
Pressure at faucet in psi = 123319 Pa / 6894.76 Pa/psi
Pressure at faucet in psi = 17.89 psi