Chapter 10 Sections 1 - 3

*A fluid is a substance that flows. Liquids and gases are fluids. *A liquid has a definite surface, but a gas does not have a definite surface. Most of the chapter deals with the study of hydrostatics … fluids at rest.

10.1 Density and Specific Gravity

*The density of an object is found by dividing its mass by its volume. Solids and liquids are nearly incompressible and thus have nearly constant density even if a compressing force acts on them. Gases have densities that vary greatly. The table on page 276 shows some density values. Note the power of 10 on some numbers. Another common unit for density is grams/cm³. Water has a density of 1 gram/cm³ or 1000 kg/m³.

What is the weight in pounds of a lead brick that has rectangular dimensions of

20 cm by 5 cm by 10 cm?

What is the specific gravity of an object that has a density of 6.5 g/cm³ ?

10.2 Pressure in Fluids

*Pressure is calculated by dividing the force which acts perpendicular to an area by the value of the area. 1 Newton/1 m² is called 1 Pascal. Place a pen or pencil between two fingers. Press (a little). Which finger feels the most discomfort? Why?

The air which is above you creates a downward force on you. The value of atmospheric pressure is about 14.7 lb/in² or about 1.013 x 10⁵ Pascals. The atmospheric pressure decreases as one moves to higher altitudes. The nature of the change is more complicated than we need to discuss in this class. It is approximately exponential.

The pressure created by a fluid is easier to calculate since the density of the fluid is nearly constant. The pressure at a certain depth, h, in a fluid is found by P = density* g * h.

What is the value of the pressure at the bottom of a city water tank that has a diameter of 18 meters and is 50 meters tall?

10.3 Atmospheric Pressure and Gauge Pressure

Gauge pressure is the pressure with respect to atmospheric pressure. When you measure the pressure of air in a tire you read the gauge pressure. The true pressure is found by adding the atmospheric and gauge pressure values. Most calculations require a true pressure, not a gauge pressure.

10-4 Pascal’s Principle

Pascal’s Principle: The pressure applied to a confined fluid increases the pressure throughout the fluid by the same amount. If the pressure increases by ( D P ) at one point in the fluid, the pressure changes by an equal amount (D P), at all points in the fluid. Pascal’s principle can be used to understand the operation of a hydraulic system. In this machine an extra pressure is created at one point in the hydraulic fluid by applying a force to a small piston. This extra pressure is then present everywhere in the fluid. At some other place in the system a large piston is used to apply force to an object. The ratio of the output force to the input force is equal to the ratio of the output piston area to the input piston area. Why?

10.5 Measurement of Pressure: Gauges and the Barometer

The barometer (see page 281) takes advantage of this fact to measure the atmospheric pressure. The atmospheric pressure is used to balance the pressure created by a column of mercury. As the atmospheric pressure varies the value of h for the mercury column varies. Why is water not commonly used for constructing this type of barometer?

10.6 Buoyancy and Archimdes’ Principle

Suppose that an object is submerged in a fluid. At what point on the object does the pressure have its largest value?

Since Force = Pressure * Area, the upward force on the object due to the fluid is greater than the downward force on the object. This difference in force is the buoyant force. Archimedes’ Principle states that the value of the buoyant force is equal to the weight of the displaced fluid. The text shows this in Figure 10-10. It is true for objects of any shape.

What volume of lead should be attached to the bottom of a pine board (mass = 1.2 kg) such that the board becomes totally submerged in sea water but does not continue to sink? Let the density of the pine board be 0.45 grams/cm³ .

Why do ships made of iron not sink? (at least when initially placed in water at the shipyard)

I will give a one point bonus to the first person who sends me e-mail that describes a Cartesian Diver. This bonus point expires at the start of class on the day we cover this page of the reading guide.

The 151 class will skip sections 7,8,9,10,11,12

10.13 Pumps; the Heart and Blood Pressure

What is the difference between a vacuum pump and a force pump?

Estimate the change in blood pressure if the reading is taking with the jacket wrapped around the lower leg (near the ankle) instead of around the upper arm.

Copyright© 2001 - 2006 by Greg Clements Permission is granted to reproduce this document as long as 1) this copyright notice is included, 2) no charge above photocopy costs is made, and, 3) the use is for an educational purpose. Editing of the document to suit your own class style and purposes is allowed.

161 only

The Equation of Continuity Beginning of Hydrodynamics

Suppose that an incompressible fluid moves through a pipe which has a change in cross sectional area. Is the velocity of the fluid different in regions where the areas are different? Is there any real world illustration of this effect?

It turns out that V₁ * A₁ = V₂ * A₂

Bernoulli’s Equation r gh + ½ r V² + P = constant

This theorem can be applied in situations in which the value of frictional force on the fluid is zero. When this is true then energy is conserved and the fluid moves in laminar flow (no turbulence). The work per volume plus the potential energy per volume plus the kinetic energy per volume will be a constant.

Copyright© 2001 - 2006 by Greg Clements Permission is granted to reproduce this document as long as 1) this copyright notice is included, 2) no charge of any kind is made, and, 3) the use is for an educational purpose. Editing of the document to suit your own class style and purposes is allowed.