Lecture 4 - Mass, weight, density, and pressure pt. 1
The derivation of pressure as a measure of energy per unit volume from its definition as Equation 2 by itself gives the pressure exerted by a liquid relative to. Pstatic fluid = ρgh where, ρ = m/V = fluid density like mmHg or cm H2O, etc. Pressures are often measured by manometers in terms of a liquid column height. Sal derives the formula to determine the pressure at a specific depth in a fluid. Density and.
What is that mass of the liquid? Well, now I'll introduce you to a concept called density, and I think you understand what density is-- it's how much there is of something in a given amount of volume, or how much mass per volume. That's the definition of density. The letter people use for density is rho-- let me do that in a different color down here.Specific gravity - Fluids - Physics - Khan Academy
The units are kilograms per meter cubed-- that is density. I think you might have an intuition that if I have a cubic meter of lead-- lead is more dense than marshmallows. Because of that, if I have a cubic meter of lead, it will have a lot more mass, and in a gravitational field, weigh a lot more than a cubic meter of marshmallows.
Of course, there's always that trick people say, what weighs more-- a pound of feathers, or a pound of lead? Those, obviously, weigh the same-- the key is the volume. A cubic meter of lead is going to weigh a lot more than a cubic meter of feathers. Making sure that we now know what the density is, let's go back to what we were doing before.
We said that the downward force is equal to the mass of the liquid times the gravitational force, and so what is the mass of the liquid? We could use this formula right here-- density is equal to mass times volume, so we could also say that mass is equal to density times volume.
I just multiply both sides of this equation times volume. In this situation, force down is equal to-- let's substitute this with this. The mass of the liquid is equal to the density of the liquid times the volume of the liquid-- I could get rid of these l's-- times gravity. What's the volume of the liquid? The volume of the liquid is going to be the cross-sectional area of the cylinder times the height. So let's call this cross-sectional area A. A for area-- that's the area of the cylinder or the foil that's floating within the water.
We could write down that the downward force is equal to the density of the fluid-- I'll stop writing the l or f, or whatever I was doing there-- times the volume of the liquid. The volume of the liquid is just the height times the area of the liquid. So that is just times the height times the area and then times gravity.
Pressure at a depth in a fluid
We've now figured out if we knew the density, this height, the cross-sectional area, and the gravitational constant, we would know the force coming down. Weight is a force and depends on both the mass of an object and the strength of gravity.
We tend to use weight and mass interchangeably because we spend all our lives on the earth where gravity never changes.
On the earth where the pull of gravity never changes, any three objects that all have the same mass even if they have different volumes and are made of different materials would always have the same weight. There is quite a bit of information hidden in the gravitational acceleration term.
How Are Density, Mass & Volume Related? | Sciencing
Click here for more details. When gravity is always the same, three objects with the same weight would also have the same mass. The difference between mass and weight is clearer perhaps if you compare the situation on the earth and on the moon. An object carried from the earth to the moon will have the same mass.
However the gravitational attraction between the object and the moon is less than on the earth. So the object weighs less on the moon than it does on the earth. Air density will come up frequently in this class. Density is defined as mass divided by volume.
In the first example there is more mass more dots in the right box than in the left box. Since the two volumes are equal the box at right has higher density.
Equal masses are squeezed into different volumes in the bottom example. The box with smaller volume has higher density. The air that surrounds the earth has mass. Gravity pulls downward on the atmosphere giving it weight.
Galileo conducted in the s a simple experiment to prove that air has weight. Pressure is defined as force divided by area. Air pressure is the weight of the atmosphere overhead divided by the area the air is resting on.
Atmospheric pressure is determined by and tells you something about the weight of the air overhead.
What is pressure?
This is one way, a sort of large scale representation, of understanding air pressure. Under normal conditions a 1 inch by 1 inch column of air stretching from sea level to the top of the atmosphere will weigh Normal atmospheric pressure at sea level is Now here's where the steel bar comes in.
The steel bar also weighs exactly Because the base of the bar has dimensions of 1" x 1" 1 square inch the pressure at the bottom of the bar is A stack of ninety four 5 pound bricks would weigh pounds. The pile of bricks is much heavier but it is also sitting on a much larger area. The pressure at the base of the brick pile would be pounds divided by 32 square inches the side of a brick has dimensions of about 4 x 8 inches or about Here are some of the other commonly used pressure units.
Pressure/Density Level Instrumentation
Typical sea level pressure is The word "bar" basically means pressure and is used in a lot of meteorological terms. Pressure at sea level is determined by the weight of the air overhead. What happens to pressure as you move upward in the atmosphere. We can use a shorter pile of bricks to help answer this question.
This makes density a useful property in identifying many substances. However, since volume deviates with changes in temperature and pressure, density can also change with temperature and pressure. Specific Gravity One derivative measurement of density is specific gravity. Specific gravity compares the density of a substance with the density of a reference material.
In the case of gases, the reference material is standard dry air, or air without water. In the case of liquids and solids, the reference material is fresh water. Specific gravity is calculated by dividing the density of a substance by the reference substance's density. For example, gold has a density of This yields a specific gravity of This means gold is Buoyancy Whether an object floats or sinks is determined by the downward force of gravity and an upward buoyant force.