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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 46
How fast does water flow from a hole at the bottom of a very wide, 5.1-m-deep storage tank filled with water? Ignore viscosity.
Guida verificata passo dopo passo1
Identify the principle governing the problem: This is a fluid dynamics problem that can be solved using Torricelli's theorem, which states that the speed of efflux of a fluid under gravity through a hole is given by \( v = \sqrt{2gh} \), where \( g \) is the acceleration due to gravity and \( h \) is the height of the fluid above the hole.
Determine the known values: From the problem, the height of the water column above the hole is \( h = 5.1 \, \text{m} \), and the acceleration due to gravity is \( g = 9.8 \; \text{m/s}^2 \).
Substitute the known values into Torricelli's formula: \( v = \sqrt{2 \cdot 9.8 \cdot 5.1} \).
Simplify the expression under the square root: Calculate \( 2 \cdot 9.8 \cdot 5.1 \) to find the value inside the square root.
Take the square root of the result from the previous step to find the speed of the water flowing out of the hole.
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Torricelli's Law
Torricelli's Law states that the speed of fluid flowing out of an orifice under the force of gravity is proportional to the square root of the height of the fluid above the opening. Mathematically, it can be expressed as v = √(2gh), where v is the exit speed, g is the acceleration due to gravity, and h is the height of the fluid column. This principle is crucial for determining the flow speed of water from the tank.
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Percorso guidato
10:20
Gauss' Law
Hydrostatic Pressure
Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it. In the context of the tank, the pressure at the hole is determined by the height of the water column, which influences the speed of the water exiting the hole. The deeper the water, the greater the hydrostatic pressure, leading to a higher flow speed.
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Percorso guidato
17:04Pressure and Atmospheric Pressure
Conservation of Energy
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In fluid dynamics, this principle applies as the potential energy of the water at height h is converted into kinetic energy as it flows out of the hole. This relationship is fundamental in deriving the equations that describe fluid flow, including the application of Torricelli's Law.
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Percorso guidato
06:24Conservation Of Mechanical Energy
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