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Chapter 2: Problem 4

A 3 -m-diameter vertical cylindrical tank is filled with water to a depth of \(11 \mathrm{m} .\) The rest of the tank is filled with air at atmospheric pressure. What is the absolute pressure at the bottom of the tank?

Short Answer

Expert verified
The absolute pressure at the bottom of the tank is \(2.092 x 10^5 Pa\).

Step by step solution

01

Identify the Given Variables

In this problem, the following variables are outlined: Depth of water, \(h = 11m\); Density of water, \(\rho = 1000 kg/m^3\); Acceleration due to gravity, \(g = 9.81 m/s^2\); Atmospheric pressure, \(P_0 = 1.013 x 10^5 Pa\).
02

Calculate Pressure from Water

First, we calculate the pressure contributed by the water at the bottom of the tank using the formula \(P = \rho gh\). This gives us: \(P_{water} = 1000 kg/m^3 * 9.81 m/s^2 * 11 m = 1.079 x 10^5 Pa\).
03

Calculate Total Pressure at Bottom

The absolute pressure at the bottom is the sum of the atmospheric pressure and the pressure due to the water column. Thus, we get: \(P_{total} = P_{atm} + P_{water} = 1.013 x 10^5 Pa + 1.079 x 10^5 Pa = 2.092 x 10^5 Pa\).

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Most popular questions from this chapter

An unknown immiszible liquid seeps into the bottom of an open oil tank. Some measurements indicate that the depth of the urknown liquid is \(1.5 \mathrm{m}\) and the depth of the oil (specific weight \(=8.5 \mathrm{kN} / \mathrm{m}^{3}\), floating on top is \(5.0 \mathrm{m}\). A pressure gage connezted to the bottom of the tank reads 65 kPa. What is the specific gravity of the unknown liquid?

A long, vertical wall separates seawater from fresh water. If the seawater stands at a depth of \(7 \mathrm{m},\) what depth of freshwater is required to give a zero resultant force on the wall? When the resultent force is zero, will the moment due to the fluid forces be zero? Explain.

The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately \(11,000 \mathrm{m}\) below the surface. Assume that the salt water density is constant at \(1025 \mathrm{kg} / \mathrm{m}^{3}\) and determine the pressure at this depth.

A studant needs to measure the air pressure inside a compressed air tenk but does not have ready access to a pressure gage. Using materials already in the lab, she builds a U-tube manometer using two clear 3 -ft-long plastic tubes, flexible hoses, and a tape measure. The only readily avai able liquids are water from a tap and a bottle of corn syrup. She selects the corn syrup because it has a larger density \((S G=1.4) .\) What is the maximum air pressure, in psia, that can be measured?

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.
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