Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo

Summary

14.1 Fluids, Density, and Pressure

  • A fluid is a state of matter that yields to sideways or shearing forces. Liquids and gases are both fluids. Fluid statics is the physics of stationary fluids.
  • Density is the mass per unit volume of a substance or object, defined as ρ=m/V.ρ=m/V. The SI unit of density is kg/m3.kg/m3.
  • Pressure is the force per unit perpendicular area over which the force is applied, p=F/A.p=F/A. The SI unit of pressure is the pascal: 1Pa=1N/m21Pa=1N/m2.
  • Pressure due to the weight of a liquid of constant density is given by p=ρghp=ρgh, where p is the pressure, h is the depth of the liquid, ρρ is the density of the liquid, and g is the acceleration due to gravity.

14.2 Measuring Pressure

  • Gauge pressure is the pressure relative to atmospheric pressure.
  • Absolute pressure is the sum of gauge pressure and atmospheric pressure.
  • Open-tube manometers have U-shaped tubes and one end is always open. They are used to measure pressure. A mercury barometer is a device that measures atmospheric pressure.
  • The SI unit of pressure is the pascal (Pa), but several other units are commonly used.

14.3 Pascal's Principle and Hydraulics

  • Pressure is force per unit area.
  • A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
  • A hydraulic system is an enclosed fluid system used to exert forces.

14.4 Archimedes’ Principle and Buoyancy

  • Buoyant force is the net upward force on any object in any fluid. If the buoyant force is greater than the object’s weight, the object will rise to the surface and float. If the buoyant force is less than the object’s weight, the object will sink. If the buoyant force equals the object’s weight, the object can remain suspended at its present depth. The buoyant force is always present and acting on any object immersed either partially or entirely in a fluid.
  • Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid it displaces.

14.5 Fluid Dynamics

  • Flow rate Q is defined as the volume V flowing past a point in time t, or Q=dVdtQ=dVdt where V is volume and t is time. The SI unit of flow rate is m3/s,m3/s, but other rates can be used, such as L/min.
  • Flow rate and velocity are related by Q=AvQ=Av where A is the cross-sectional area of the flow and v is its average velocity.
  • The equation of continuity states that for an incompressible fluid, the mass flowing into a pipe must equal the mass flowing out of the pipe.

14.6 Bernoulli’s Equation

  • Bernoulli’s equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid:
    p1+12ρv12+ρgh1=p2+12ρv22+ρgh2.p1+12ρv12+ρgh1=p2+12ρv22+ρgh2.
  • Bernoulli’s principle is Bernoulli’s equation applied to situations in which the height of the fluid is constant. The terms involving depth (or height h) subtract out, yielding
    p1+12ρv12=p2+12ρv22.p1+12ρv12=p2+12ρv22.
  • Bernoulli’s principle has many applications, including entrainment and velocity measurement.

14.7 Viscosity and Turbulence

  • Laminar flow is characterized by smooth flow of the fluid in layers that do not mix.
  • Turbulence is characterized by eddies and swirls that mix layers of fluid together.
  • Fluid viscosity ηη is due to friction within a fluid.
  • Flow is proportional to pressure difference and inversely proportional to resistance:
    Q=p2p1R.Q=p2p1R.
  • The pressure drop caused by flow and resistance is given by p2p1=RQp2p1=RQ.
  • The Reynolds number NRNR can reveal whether flow is laminar or turbulent. It is NR=2ρvrηNR=2ρvrη.
  • For NRNR below about 2000, flow is laminar. For NRNR above about 3000, flow is turbulent. For values of NRNR between 2000 and 3000, it may be either or both.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction
Citation information

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.