In this section we investigate and learn about the mass of our water rocket.

When we build our machines one of the most important characteristics is the size. That is
generally stated as the mass. When making flying machines, mass may be the single most
important attribute. When we intend to lift something off the ground, we need to know the
force required to lift it.

After finding those definitions write this sentence and fill in the blank: "The tare weight of our rocket is ______." You can probably guess it, but please look it up and be certain. You have sufficient information to write that down. We will get to the gross mass and net mass shortly.

Think about things I may have left out and measurements I might have done, and even mistakes I might have made. Write those down and make those measurements. Please bring your documents and your ideas to class.

Let us begin!

We will begin with the easiest one first, the mass of our bottle. The water rocket kit was purchased from Hobby Lobby. I filled the bottle with water then measured the amount to be 1.25 liters. Not having a small scale, an Internet search revealed that the mass of a 1.25 liter plastic water bottle is 42 grams. We will make some rockets with two liter bottles. Do some Google searches and discover their mass.

Water is very important to scientific standards. 1 cm^{3} of water has a mass of 1 gram.
That relationship was created on purpose and did not just happen that way.

If we make a cube of water that is 10 cm on each of the sides, the volume of the box
is 10cm * 10cm * 10cm or 1000 cm * cm * cm or 1000 cm^{3}. That is one liter of water. It contains
1000 cm^{3} of water. Therefore it has a mass of 1000 grams or one kilogram.

Find out if you have a measuring cup in the house and see if it has liters marked on it. If not you can search the Internet and discover that one quart is about 0.95 liters. A quart is just a little bit smaller than a liter and a little bit less mass. How many drinking glasses will a liter of water fill?

The word kilogram is the word **gram** with the prefix **kilo** added to it. Kilo means one thousand
so one kilogram is 1000 grams. For reference, one kilogram weighs about 2.2 pounds. A gram is pretty small.
One medium sized paper clip has the mass of about one gram.

We estimated that the best flight was with our rocket filled about half full of water. For convenience
let us presume we are starting with 500 cc of water which has a mass of 500 grams. (Note: cc is short
for cubic centimeter or cm^{3}.)

How much volumn is left over for the air? Please calculate it yourself before you continue. And write it down in complete sentences.

To calculate the answer remember that the bottle capacity is 1.25 liters. Convert that to cc and
the bottle volume is 1250 cm^{3}.

When 500 cm^{3} are occupied by the water there are 750 cm^{3} remaining for the air.

See if you can discover the mass of air on your own. You can use a dictionary, encyclopedia, or an Internet search. Do not ask anyone, discover for yourself. It means more when you do it yourself.

Please do that before you continue.

Start a Google search and enter the phrase

But do not get too side-tracked. If you have many burning questions, write them down on another sheet of paper and look them up after you finish this section about our rockets. Bring your questions to class so we can hear what else you discovered.

As we saw in our very first experiment, the air we breathe has mass.
The density of air at sea level is 1.225 kilograms/m^{3}. We live very close to sea level so
that value will do nicely.

How much air is that? Measure a square on the floor that is about 39 inches on each side. Then
measure up for 39 inches and imagine a cardboard box that size. That is a pretty big box. The
volume of air inside would be one cubic meter or 1m^{3}

**Challenge:** How many liters of air are in a cubic meter?

Hint: A liter is a cube that is 10 centimeters on a side. A centimeter is a combination of
two phrases: **centi** and **meter**. The phrase **centi** means one hundred.
There are one hundred centimeters in a meter. If we have ten liters of air in perfect cubes,
then how many do we line up to make a line one meter long. That would be 10. Now how many
of these cubes would it take to cover the bottom of our cubic meter box?

Continue that line of thinking and you can do the calculations.

I'll wait for you.

Did you get 10 * 10 * 10 = **1000 liters per m ^{3}?**

Hopefully so.

In this lesson we will be working with liters of air rather than a cubic meter. So what is the mass of air in one liter of volume?

**Method** Convert the mass of the cubic meter of air to grams rather than kilograms to get 1,225 grams.
Divide 1,225 grams that by 1000 because there are 1000 liters in a cubic meter and we have 1.225 grams of
mass per liter of air.

Just for fun, recall that a liter of air has 1.225 grams of mass and the same volume of water has 1000 grams of mass. Divide that 1.225 grams of air in one liter into the 1,000 grams of water in one liter and quotient is 800. Water is 800 times as dense as air.

Done?

Here is one way to figure it out.
The volume of air was 750 cm^{3} while a liter of air has 1000 cm^{3}. That means
there there are 0.750 liters of air in the bottle. Multiply that by the mass of one liter of air 1.225 grams. The
result is 0.91875 grams of air in the bottle.

You might have calculated the mass of air in one cc, then multiplied by 750 to get the result. If so,
that was good thinking.

Understanding this is very important. Make sure you can do those calculations before you continue.

**Now to pressurize our rocket**

We used a pump to force more air into the bottle until the pressure was about 25 psi
(pounds per square inch) more than normal air pressure. We will work on this for a while.

After reading that, write a quick note from memory describing what a

For completeness, I'll include it here. One pascal is enough pressure to press on one square meter with a force of one newton.

Do you remember the newton? When you hold an average size apple gravity pulls it down with the force of about one newton. One newton spread out over an entire square meter is not much force.

(Note: 1 meter is 39.3701 inches so one square meter is 39.3701 inches * 39.3701 inches or 1,550.00477401 inches

One psi on each of the 1550 square inches in a square meter is a lot of pressure, 1,550 pounds on that square meter.

We are not there yet, but we are getting closer. We have determined that 1 psi on a square
meter is 1550 pounds. But pascals are a measure of newtons. Search for **convert pounds to
newtons**.

I presume you found that one pound of force is is 4.44822162 newtons. Now multiply that 1550 number by this new 4.4 number to get: (Do it your self first,...) 6894.7647468545.

**Important:** We are almost done with our conversion, but we have an intermediate product
that is very important. We know that one psi is equal to **6894.76** pascal.
This is the **conversion factor** from psi to pascal.
To convert psi to pascal, simply multiply the psi by this conversion factor. The result is
the pressure in units of **pascal**.

Now we finish our problem calculating standard air pressure in psi to pascal.

Multiply our sea level air pressure of 14.7 by the conversion factor **6894.76**
to get about 101,325. We have now reached our goal: Air pressure at sea level is 101,325 pascal.

That is a pretty big number so science often use the term **kilopascal**. That is 1000 pascal
so our pressure becomes 101.3 KPa. That is easier to work with. (Note: When reading this
you can say **K P a**, pronouncing each letter, or you can say **kilopascal** as one word.)

**Back To Our Pump**

Our pump showed the pressure as about 25 psi. To convert to pascal multiply 25 by
the conversion factor we just found: 6894.75 to get 172,368.75 pascal.

Then divide by 1000 and round off to one decimal place to get 172.3 KPa.
This is the approximate pressure in our rocket when it launched.

The end result is that we changed 25 psi to 172.3 KPa. Be sure you understand what just happened before we continue.

Think about why that is the case.

In order to push the water out of the bottle, the air pressure in the bottle must
be greater than the air pressure outside the bottle. That larger pressure on the inside is what forces
the water out.

The bicycle pump pressure gauge is a certain type of gauge known as **psig** which
stands for **Pounds per Square Inch Gauge**. It shows the pressure above ambient.
When we want to know the total pressure we use a gauge of the type **psia** or
**Pounds per Square Inch Absolute**.

We will see why that is important now.

We pumped the air pressure up to 172.3 KPa according to the gauge. But the real total pressure
was 101.3 KPa (sea level air pressure) plus what the gauge showed, 172.3 KPa for total of **273.6 KPa**.

The next question is: How much did we increase the pressure by. We take our final pressure of 273.6 (Absolute and not Gauge) and divide it by our starting pressure of 101.3 (also absolute) to get about 2.7. If we had tried to start with zero, we would be dividing by zero and that does not work out well.

But that is not the entire story. Here is the complete division problem with units of measure.

273.6 KPa _________ 101.3 KPaWe divided a pressure by another pressure. Both must have the same units of measure. Observe that this division problem included KPa divided by KPa which is a factor of one. Remember that when multiplying and dividing we can remove factors of one.

The next step is to reduce our fraction. We divide both the numerator and the denominator by 101.3 and the complete result is:

2.7 ____ 1That is the ratio. We know that anything divided by 1 is itself so for convenience, we omit the

Cool. Right? Write down any question you have before your forget them.

From our notes above we discovered that the density of air is 1.225 kilograms/m^{3}.
We also discovered that the unpressurized mass of air in our bottle was about 0.6125 grams.

From just above, we know that we increased the pressure by the ratio of 2.7 to 1. By pressurizing the
air we increased its density by a factor of 2.7. So to find our how much air we then had
in our rocket, start with the unpressurized mass of 0.91875 and multiply by 2.7 to get
about 2.48 grams of air.

42 grams the bottle 500 grams the water 2.48 grams the air ______________ 544.48 grams rocket at launchThis is the gross mass of our rocket at launch.

Hint: To find something that you know is in this document, press and hold down the Ctl key, then press the F key. That will open a find window. Type what you are searching for in the window and press the enter key. The computer will show you the next instance of those characters.

You probably noticed that the mass of the fins are not included. How would you categorize their mass?

Water Rocket Thrust

12 Jan 2015

Bryan Kelly

send comments to: on line at bkelly dot ws