A 30 -ft-high downspout of a house is clogged at the bottom. Find the pressure at the bottom if the downspout is filled with \(60^{\circ} \mathrm{F}\) rainwater.

Short Answer

Expert verified
The pressure at the bottom of the downspout is 1.88 atmospheres.

Step by step solution

01

Determine the density of rainwater at given temperature

At a temperature of \(60^{\circ} F\) the density of rainwater is roughly \(0.99907 g/cm^{3}\) or \(999.07 kg/m^3\).
02

Convert the height of the downspout from feet to meters

As the height of the downspout is given in feet, convert it to meters by using the conversion factor of 1 foot = 0.3048 meters. Hence, 30 feet = 9.144 meters.
03

Calculate the pressure due to the height of the rainwater

By using the formula for pressure: P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the column of liquid, we get P = 999.07 kg/m{3} * 9.81 m/s{2} * 9.144 m = 89252.40 Pa or 0.88 atmospheres.
04

Add the atmospheric pressure

Assuming that the downspout is open at the top, the atmospheric pressure also needs to be considered. Standard atmospheric pressure at sea level is roughly 1 atmosphere. So, the total pressure at the bottom of the downspout equals the atmospheric pressure plus the pressure due to the height of the rainwater, which is 1 + 0.88 = 1.88 atm.

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