what is the equation of weight density?

Question

the equation for mass density is

density = weight(pounds)
volume(ft^3)... but does anyone know the equation for weight density?

Answer 1

Density = mass / volume

In SI units, …
Mass has units of kilograms (kg),
Volume has units of cubic meters (m^3),
So density has units of kg / m^3.

“Weight” is a force…the force of gravity exerted on the object.
Weight = mass * gravity
Where “gravity” is the gravitational acceleration experiences by the object with SI units of meters per second squared (m/s^2).
Weight has units of kg m/s^2, otherwise known as Newtons.

If you want to express a density in terms of an object’s weight instead of its mass (as would usually be the case), simply multiply the normal, mass, density by the gravitational acceleration (g = 9.81 m/s^2, on the surface of Earth), or calculate it by first finding the object’s weight and then dividing by its volume.

Above, I used SI units, but there are (for better or worse) other systems of units out there which can also be used.
If you want to convert between the two, this site will help (and/or you could just learn the conversion factors),
http://www.digitaldutch.com/unitconverter/
The formulas will still hold no matter what system of units you are in, although (of course) the input units will affect the units your answer will be in.

Answer 2

Density is by definition mass per unit volume. Therefore, you divide the mass by the volume.

You can also use weight per unit volume. Make sure you keep track of your units. If the density is required in another unit, then you need to convert them as well.

Answer 3

Oh, my goodness! Do we ever need some definitions!

Mass is how much there is of something.

Weight is the pull of gravity on a mass.

Density is the mass per unit volume.

A pound is a measurement of weight, not mass.

The formula for Density is: D = mass/volume

If you were on the moon, your mass would be the same as it is on earth, but your weight would be less than on earth because the pull of gravity on the moon is less than it is on earth.

Mass and weight are not interchangeable terms.

The units for mass is grams.
The units for weight is pounds.
The standard units for density is g/cm3

Hope this clears the air some for you.

CHEMISTRY TEACHER

Answer 4

Ok...

mass density is:

Mass density = (MASS)/(volume).

Weight Density is:

Weight Density = (WEIGHT)/(Volume).

The difference comes from the fact that the American units mass is calculated from weight. (i.e. you mass is calculated as a multiple of you mass on earth as a result from your weight on earth).

and in the SI units your weight is calculated from you mass (mass is universal).

some people have huge problems with this (especially the quantum and relativity people), but actually it does work...(it makes the calculations much, more complex).

Answer 5

density is equal to weight over volume. .

Answer 6

Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume.

Answer 7

weight density = force / volume

It is represented by a "vertical alpha" (not sure what Greek letter it is) and has units N / m^3.

It is used in engineering calculations.

Answer 8

What is density altitude?

The density altitude is the altitude at which the density of the International Standard Atmosphere (ISA) is the same as the density of the air being evaluated. (The Standard Atmosphere is simply a mathematical model of the atmosphere which is standardized so that predictable calculations can be made.)

So, the basic idea of calculating density altitude is to calculate the actual density of the air, and then find the altitude at which that same air density occurs in the Standard Atmosphere.

In the following paragraphs, we'll go step by step through the process of calculating the actual density of the air, and then determining the corresponding density altitude.

And finally, at the very end of this article, we'll compare the accurate density altitude calculations with the results of a greatly simplified equation that ignores the effects due to water vapor in the air.

Some different meanings of the word "altitude":

An aircraft altimeter measures only air pressure... nothing else. If the air pressure changes, due to temperature or humidity, then an aircraft altimeter will of course change to indicate the actual air pressure. Nonetheless, the aircraft altimeter is simply measuring air pressure.

As odd as it may seem, an aircraft altimeter does not actually measure altitude, it only measures pressure. Hence, the name "pressure altitude" is properly applied to any aircraft altimeter reading.

For pilots, it is very important to understand that an aircraft altimeter only measures air pressure (not altitude). This point is especially important to understand with the advent and use of GPS. An aircraft flying at a specific pressure altitude (as indicated by an altimeter) may note some other altitude displayed on the GPS (which measures actual distance above mean sea level). In some cases this difference is small... but in some cases it could be enough to cause a mid-air collision if a pilot was flying on a GPS altitude rather than pressure altitude. (To solve that problem, some GPS units do include an air pressure sensor so that they can indicate pressure altitude.)

Therefore, it is crucial to always verify what is meant by "altitude", and differentiate a pressure-based measurement of "pressure altitude" from a distance-based measurement of actual altitude.

Density altitude is a concept based on solely on air density, and is neither "pressure altitude" nor "mean sea-level altitude", but is strictly "density altitude".

Now... on to Density Altitude.....


Density and Density Altitude:

Although the concept of density altitude is commonly used to help express the effects of aircraft performance, the really underlying property of interest is actually the air density.

For example, the lift of an aircraft wing, the aerodynamic drag and the thrust of a propeller blade are all directly proportional to the air density. The downforce of a racecar spoiler is also directly proportional to the air density. Similarly, the horsepower output of an internal combustion engine is related to the air density. The correct size of a carburetor jet is related to the air density, and the pulse width command to an electronic fuel injection nozzle is also related to the air density.

Density altitude has been a convenient yardstick for pilots to compare the performance of aircraft at various altitudes, but it is in fact the air density that is the fundamentally important quantity, and density altitude is simply one way to express the air density.

(Note: If you're just hunting for a simple, but not very accurate, approximation for density altitude, be sure to study the "Simpler Methods of Calculation" section near the end of this article.)


Units:

The 1976 International Standard Atmosphere is mostly described in metric SI units, and I have chosen to use those same units (in general). See ref 8 and ref 9 for conversion factors to your favorite units.


Air Density Calculations:

To begin to understand the calculation of air density, consider the ideal gas law:

(1) P*V = n*R*T

where: P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature


Density is simply the number of molecules of the ideal gas in a certain volume, in this case a molar volume, which may be mathematically expressed as:

(2) D = n / V

where: D = density
n = number of molecules
V = volume


Then, by combining the previous two equations, the expression for the density becomes:

(3)

where: D = density, kg/m3
P = pressure, Pascals ( multiply mb by 100 to get Pascals)
R = gas constant , J/(kg*degK) = 287.05 for dry air
T = temperature, degK = deg C + 273.15


As an example, using the ISA standard sea level conditions of P = 101325 Pa and T = 15 deg C, the air density at sea level, may be calculated as:

D = (101325) / (287.05 * (15 + 273.15)) = 1.2250 kg/m3

This example has been derived for the dry air of the standard conditions. However, for real-world situations, it is necessary to understand how the density is affected by the moisture in the air.

The density of a mixture of dry air molecules and water vapor molecules may be expressed as:

(4)

where: D = density, kg/m3
Pd = pressure of dry air, Pascals
Pv= pressure of water vapor, Pascals
Rd = gas constant for dry air, J/(kg*degK) = 287.05
Rv = gas constant for water vapor, J/(kg*degK) = 461.495
T = temperature, degK = deg C + 273.15

To determine the density of the air, it is necessary to know is the actual air pressure (also known as absolute pressure, or station pressure), the water vapor pressure, and the temperature.

It is possible to obtain a rough approximation of the absolute pressure by adjusting an altimeter to read zero altitude and reading the value in the Kollsman window as the actual air pressure, but this method only gives the correct reading if the ambient air temperature happens to be the same as standard temperature at your elevation. Near the end of this page I'll discuss how to use the altimeter reading to accurately determine the actual pressure.

Alternatively, there are many little electronic gadgets that can measure the actual air pressure directly, and quite accurately. The water vapor pressure can be determined from the dew point or from the relative humidity, and the ambient temperature can be measured in a well ventilated place out of the direct sunlight.

In the following section, we'll calculate the portion of the total air pressure that is due to the water vapor in the air that is being measuring.


Vapor Pressure:

A very accurate, albeit quite odd looking, formula for determining the saturation vapor pressure is a polynomial developed by Herman Wobus (see ref 2 ) :

(5) Es = eso / p8

where: Es = saturation pressure of water vapor, mb
eso=6.1078
p = (c0+T*(c1+T*(c2+T*(c3+T*(c4+T*(c5+T*(c6+T*(c7+T*(c8+T*(c9))))))))))
T = temperature, deg C
c0 = 0.99999683
c1 = -0.90826951*10-2
c2 = 0.78736169*10-4
c3 = -0.61117958*10-6
c4 = 0.43884187*10-8
c5 = -0.29883885*10-10
c6 = 0.21874425*10-12
c7 = -0.17892321*10-14
c8 = 0.11112018*10-16
c9 = -0.30994571*10-19


For situations where a slightly less accurate formula is acceptable, the following equation offers good results, especially at the higher ambient air temperatures where the saturation pressure becomes significant for the density altitude calculations.

(6)

where: Es = saturation pressure of water vapor, mb
Tc = temperature, deg C
c0 = 6.1078
c1 = 7.5
c2 = 237.3

See ref 2 and ref 11 for additional vapor pressure formulas.

Here's a calculator that evaluates the saturation vapor pressure using equations 5 and 6 as given above:


The Smithsonian reference tables (see ref 1) give the following values of saturated vapor pressure values at specified temperatures. Entering these known temperatures into the calculator will allow you to evaluate the accuracy of the calculated results.
Deg C Es, mb
30 42.430
20 23.373
10 12.272
0 6.1078
-10 2.8627
-30 0.5088

Armed with the vapor pressure equations, the next step is to determine the actual value of vapor pressure.

When calculating the vapor pressure, it is often more accurate to use the dew point temperature rather than the relative humidity. Although relative humidity can be used to determine the vapor pressure, the value of relative humidity is strongly affected by the ambient temperature, and is therefore constantly changing during the day as the air is heated and cooled.

In contrast, the value of the dew point is much more stable and is often nearly constant for a given air mass regardless of the normal daily temperature changes. Therefore, using the dew point as the measure of humidity allows for more stable and therefore potentially more accurate results.


Actual Vapor Pressure from the Dew Point:

To determine the actual vapor pressure, simply use the dew point as the value of T in equation 5 or 6. That is, at the dew point, Es = Pv.

(7) Es = Pv at the dew point


Actual Vapor Pressure from Relative Humidity:

Relative humidity is defined as the ratio (expressed as a percentage) of the actual vapor pressure to the saturation vapor pressure at a given temperature.

To find the actual vapor pressure, simply multiply the saturation vapor pressure by the percentage and the result is the actual vapor pressure. For example, if the relative humidity is 40% and the temperature is 30 deg C, then the saturation vapor pressure is 42.43 mb and the actual vapor pressure is 40% of 42.43 mb, which is 16.97 mb.


Density Calculations:

Now that the actual vapor pressure is known, we can calculate the density of the combination of dry air and water vapor as described in equation 4.

The total measured atmospheric pressure is the sum of the pressure of the dry air and the vapor pressure:

(8) P = Pd + Pv

where: P = total pressure
Pd = pressure due to dry air
Pv = pressure due to water vapor

So, rearranging that equation, we see that Pd = P-Pv. Now we have all of the information that is required to calculate the air density.


Calculate the air density:

Now armed with those equations and the actual air pressure, the vapor pressure and the temperature, the density of the air can be calculated..

Here's a calculator that determines the air density from the actual pressure, dew point and air temperature using equations 4, 6, 7 and 8 as defined above: