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19. Fluid Mechanics

Pressure Gauge: Barometer

Physics

19. Fluid Mechanics

Pressure Gauge: Barometer

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2:36 minutes

Problem 19

Textbook Question

Determine the minimum gauge pressure needed in the water pipe leading into a building if water is to come out of a faucet on the fourteenth floor, 44 m above that pipe.

Verified step by step guidance

Identify the key concept: The problem involves determining the minimum gauge pressure required to lift water to a height of 44 m. This is a fluid mechanics problem that uses the relationship between pressure, height, and density in a static fluid.

Use the hydrostatic pressure formula: The pressure required to lift a fluid to a certain height is given by the equation:

P = ρ g h

, where

ρ

is the density of water (approximately 1000 kg/m³),

g

is the acceleration due to gravity (9.8 m/s²), and

h

is the height (44 m).

Substitute the known values into the formula: Replace

ρ

with 1000 kg/m³,

g

with 9.8 m/s², and

h

with 44 m in the equation

P = ρ g h

Recognize that the result from the formula gives the absolute pressure due to the water column. To find the gauge pressure, note that gauge pressure excludes atmospheric pressure. Since the problem asks for the minimum gauge pressure, the atmospheric pressure is not added to the result.

Conclude the calculation: After substituting the values and performing the multiplication, the result will give the minimum gauge pressure in Pascals (Pa). Ensure the units are consistent throughout the calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gauge Pressure

Gauge pressure is the pressure relative to atmospheric pressure. It is the pressure measured in a system that excludes the atmospheric pressure acting on the fluid. In this context, it is crucial to determine how much additional pressure is needed in the water pipe to ensure that water can reach the faucet on the fourteenth floor.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. It increases with depth in a fluid and is calculated using the formula P = ρgh, where P is the pressure, ρ is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column. This concept is essential for calculating the pressure needed to lift water to a specific height.

Bernoulli's Principle

Bernoulli's Principle states that in a flowing fluid, an increase in velocity occurs simultaneously with a decrease in pressure or potential energy. This principle helps in understanding how pressure changes in a fluid system, which is important when considering the flow of water from the pipe to the faucet at a higher elevation.

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Related Practice

Textbook Question

What is the height of a water barometer at atmospheric pressure?

Multiple Choice

A classic barometer (shown below) is built with a 1.0-m tall glass tube and filled with mercury (13,600 kg/m³). Calculate the atmospheric pressure, in ATM, surrounding the barometer if the column of liquid is 76 cm high. (Use g=9.8 m/s².)

The liquid in the open-tube manometer in Fig. 12.8a is mercury, y₁=3.00 cm,and y₂=7.00 cm. Atmospheric pressure is 980 millibars. What is (a) the absolute pressure at the bottom of the U-shaped tube; (b) the absolute pressure in the open tube at a depth of 4.00 cm below the free surface; (c) the absolute pressure of the gas in the container; (d) the gauge pressure of the gas in pascals?

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Textbook Question

A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61° from the horizontal (Fig. 13–53). How high could the water shoot if it came vertically out of a broken pipe in front of the house?

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Textbook Question

A 3.2-N force is applied to the plunger of a hypodermic needle. If the diameter of the plunger is 1.3 cm and that of the needle is 0.20 mm, with what force does the fluid leave the needle?

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views

Textbook Question

A house at the bottom of a hill is fed by a full tank of water 6.0 m deep and connected to the house by a pipe that is 75 m long at an angle of 61° from the horizontal (Fig. 13–53). Determine the water gauge pressure at the house.

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views

Textbook Question

What is the height of a water barometer at atmospheric pressure?

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