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What is the volume rate of flow of water from a 1.85-cm-diameter faucet if the pressure head is 12.0 m?
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Ch. 13 - Fluids
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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TOC.tableOfContents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 13, Problema 45
A 12-cm-radius air duct is used to replenish the air of a room 8.2 m x 4.5 m x 3.5 m every 12 min. How fast does the air flow in the duct?
Guida verificata passo dopo passo1
Calculate the volume of the room using the formula for the volume of a rectangular prism: \( V = l \cdot w \cdot h \), where \( l = 8.2 \ \text{m} \), \( w = 4.5 \ \text{m} \), and \( h = 3.5 \ \text{m} \).
Determine the air flow rate required to replenish the room's air every 12 minutes. Convert 12 minutes to seconds (\( t = 12 \cdot 60 \ \text{s} \)) and use the formula \( Q = \frac{V}{t} \), where \( Q \) is the volumetric flow rate.
The air duct is cylindrical, so calculate the cross-sectional area of the duct using the formula for the area of a circle: \( A = \pi r^2 \), where \( r = 12 \ \text{cm} = 0.12 \ \text{m} \).
Relate the volumetric flow rate \( Q \) to the air velocity \( v \) in the duct using the formula \( Q = A \cdot v \). Rearrange this equation to solve for \( v \): \( v = \frac{Q}{A} \).
Substitute the values for \( Q \) and \( A \) into the equation for \( v \) to find the air velocity in the duct. Ensure all units are consistent (e.g., meters, seconds).
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Airflow Rate
Airflow rate is the volume of air that moves through a duct per unit of time, typically measured in cubic meters per second (m³/s). To find the airflow rate, one can divide the total volume of air exchanged by the time taken for that exchange. In this case, the volume of the room must be calculated first to determine how much air is replenished every 12 minutes.
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Percorso guidato
6:34
Fluid Speed & Volume Flow Rate
Cross-sectional Area of the Duct
The cross-sectional area of a duct is the area of the circular opening through which air flows. It can be calculated using the formula A = πr², where r is the radius of the duct. For a 12-cm radius duct, this area is crucial for determining the velocity of the air flowing through the duct, as it relates the volume flow rate to the speed of the air.
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08:10Calculating the Vector (Cross) Product Using Components
Velocity of Airflow
The velocity of airflow is the speed at which air moves through the duct, typically expressed in meters per second (m/s). It can be calculated by dividing the airflow rate by the cross-sectional area of the duct. Understanding this concept is essential for determining how quickly air is replenished in the room, which is a key part of the problem.
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7:27Escape Velocity
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