Fluid Power –How Hydraulics Can Move Mountains

Many people may not realize the potential power that they hold in a glass of water.  If you really look closely at the power of fluids, like water, you’ll see how they have the ability to literally move mountains.  Examples are everywhere in nature.  One of the best examples of how powerful a fluid can be is the Grand Canyon.  With enough time, water can carve out vast parts of our landscape.  And it didn’t take long for humans to harness fluid power in the form of hydraulics.

Hydraulics is a term used for the application of fluid power in a liquid form.  After all, gas is also a fluid.  When you look at gas as a fluid power, it is referred to as pneumatic.  Hydraulics is most commonly used in machinery.  The advantage of using hydraulics in machinery is the ability to move, cut, carry, lift, dig, or mix a very large load.  In machinery the hydraulics form a system made up of a pump to move the fluid, hoses or pipes for the fluid to move through, and a hydraulic actuator that performs work.  The two most common types of actuators in hydraulics are cylinders and motors.

Before we can get into how the hydraulic motors and cylinders work, we need to understand two aspects of hydraulic power: pressure and flow.  Pressure is the amount of force that is being transmitted through a fluid and can be calculated as pounds per square inch (PSI).  If you apply 1000 pounds onto one square inch of area, you have 1000 PSI.  Flow is the amount of volume and speed in which you are moving the fluid, and is many times calculated as Gallons per Minute (GPM).  If you are pumping 20 gallons of fluid every minute, your flow is 20GPM.  In hydraulics, horsepower is calculated from pressure and flow.

Calculate Hydraulic Horsepower

A hydraulic cylinder is basically a rod that is inside a sealed tube.  As the tube is filled with fluid, it forces the rod out of the tube.  Cylinders are everywhere in machinery and can push and pull very large loads of weight.  Think of a fork truck and the cylinders used to lift the load.  The force that the cylinder can exert depends on cylinder size and the amount of pressure being applied.  The amount of speed that the rod moves out at is determined by cylinder size and the flow of the fluid.
 Calculate Cylinder Force  Calculate Cylinder Speed

A hydraulic motor is very similar to a pump.  A pump is being turned by electrical, mechanical, or even human power to create pressure and flow in the fluid.  A motor converts the pressure and flow back to a rotating output.  Many times motors are mounted to wheels, augers, or mixers.  Think of the drum on a cement truck.  That is a heavy load being turned.  The amount of torque the motor is able to produce depends on the motor displacement and the pressure of the fluid.  The speed of the motor also depends on the motor displacement, but depends on fluid flow.

 Calculate Hydraulic Motor Torque  Calculate Hydraulic Motor Speed

Now you have the basics of how hydraulics work and why they are used on heavy machinery.  The next time you drive by a construction site and see the large machinery, think about the river in the Grand Canyon and how powerful fluids really can be.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Circle Math - A Well Rounded Education

There are a lot of clichés to choose from for a blog about circle math.  What goes around comes around, a new spin on math, or it’s easy as PI.  Regardless of the corny ways to describe the subject, there is no denying the importance of knowing the basic math associated with circles.  We rely on circles heavily in our daily lives.  Imagine a world without wheels, circular planets, and (most important to me) round food like pizza and hamburgers.  There are so many aspects in our lives that we rely on circles and spheres that is why it is important to know the basic math associated with them.

The most important mathematical ingredient to understand on this subject is Pi.  This is a constant number used when calculating different aspects of circles.  The actual number of Pi is approximately 3.141592654….it actually has a never ending amount of numbers after the decimal.  In most math classes it suffices to use 3.14 or 3.1416 for more specific answers.

 In addition to PI, there is the radius and diameter.  The radius is the amount of distance from the center of the circle to the outside of the circle.  The diameter is the distance of a line that bisects the circle from one side to the other and crosses through the center.  The diameter of a circle is always twice the distance as the radius.
 
There are no corners, or even sides to this shape.  It is a continuous curve around a common point.  The outside of a circle is called a circumference.  It’s similar to the perimeter of other shapes, but since there isn’t a side, just a constant curve, it’s called a circumference.  To calculate the circumference of a circle you need to know the radius length and Pi.  The equation is:  2 x Pi x R where R is the radius.  Sometimes you’ll also see this equation used with the diameter.  Because the diameter is twice the distance as the radius, the equation would be: Pi x D where D is the Diameter.

 The area of a circle is also important.  ( I want to know how much pizza I’m eating )  To calculate the area of a circle, you can use Pi and the radius again.  The equation to find the area is: Pi x R².  If you take the square of the radius and multiply that by Pi you will have the area. 

 Since the sphere is the 3-D version of the circle, the math to calculate the surface area and volume only slightly more complex.  You can use the following equation to calculate the surface area of a sphere:  4 x Pi x R².  To calculate the volume of a sphere, use the equation:   4/3 x Pi x R³.

 Now you have the basic math for circles and spheres.  What you can do with this mathematical power is nearly limitless.  You can calculate the volume of the Earth, you can calculate the surface area of a baseball, or like me, you can find out the area of a pizza.


CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Basic Math of Triangles

It's hard to imagine a world without the triangle.  I'm not talking about the musical instrument version, the love version, or even the famous Bermuda version.  If you really think about how many uses you see for triangles in every aspect of our lives, it would be scary to imagine a world without them.  They are used in engineering, architecture, machinery, nature and decorations.  Because there are so many uses, it is important to have a strong grasp of the basic math principles behind this shape.

A triangle is a 3 sided shape with 3 corners and can be described in 3 ways.  There are three basic types: Isosceles, Scalene and Equilateral.  An Equilateral triangle has equal lengths on all 3 sides.  An Isosceles has 2 sides of equal length.  And Scalene has 3 different lengths of all sides.

A unique triangle is the Right triangle.  This triangle has one corner that is 90 degrees.  No matter what version you have, you can add all 3 angles at the corners and the sum will be 180 degrees.

To find the perimeter you find the total sum of the lengths of all three sides.  It's pretty simple.  To calculate the triangle perimeter you add  Length1 + Length2 + Length3.

The area of a triangle is a little more tricky.  Think of a triangle as half of a parallelogram.  To calculate the area of a parallelogram, you multiply the base length by the height.  Don't confuse the height length as one of the side lengths.  To calculate the area of triangle , you multiply 1/2 x base length x height.

Finally we get to the Pythagorean Theorem.  On any triangle, the longest side is referred to as the hypotenuse.  If you look at a Right triangle, the hypotenuse is directly across from the 90 degree angle.  Using the Pythagorean Theorem, we can calculate the length of the hypotenuse of the Right Triangle from the lengths of the other two sides.  To calculate the hypotenuse (c), use the equation: a² + b² = c²

These are some of the most basic math calculations for triangles.  Try to spend a day and make a list of how many times you see a triangle in use.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Is The Pay Worth the Pain? Salary vs. Hourly Wage

I’m sure there are many people that ask themselves if they are getting paid enough.  It would be rare for someone to say that they felt that they didn’t need more pay.  But, how much is your time and effort worth?  If you get paid hourly wages, you can get extra money for working longer hours.  If you work at a job that pays a salary, you may be required to work many late nights, or put in extra effort without an increase in pay.  There are a lot of jobs out there that are very similar in function, but they may pay either a salary, or hourly wages.  What is worth more?

First, there must be some assumptions.  Most of the time, the total compensation at a job can include benefits other than just pay. There are things like insurance, vacations, sick days, etc.  Those are definitely factors that can make a difference on how well someone feels they are being compensated.  But, if all of those factors are fairly equal in the level of compensation, it is pretty easy to determine what method of earnings would be better.

To calculate the yearly income of most people earning a salary, it is fairly straight forward.  The yearly salary is generally a set amount of money that a person earns in a year, usually taken in monthly, bi-monthly, or weekly increments.  This yearly amount doesn’t change whether a person puts in extra hours, or fewer hours.  Of course there is a job function that needs to be done and if a person isn’t putting in the necessary time to accomplish their tasks, they could soon be earning $0 for a yearly salary.

Now a typical hourly wage job is based on a rate of pay, like dollars per hour.  The amount that someone could earn in a year is going to be affected by their pay rate and the amount of hours that they work in a year.  Another factor that enters into the equation is overtime pay.  In the U.S., a normal work week is 40 hours.  Every hour that is worked in addition to 40 hours is considered overtime and the pay rate for those extra hours is 150% of your normal pay rate.  Typically it’s called “time and a half”.

So now that you have a better idea of both pay practices, we can compare them to see which is better for a given situation.  Of course, this is not taking into account other compensation benefits.

Here is an example:  A paralegal is paid $18.50/hour in hourly wages, and is working for a new lawyer that is paid $65,000 in annual salary.  They spend a year working the same amount of long hours to prepare for a high profile case.  If they are at the office 12 hours/day, 5 days/week, 50 weeks a year, how does their pay compensation compare?

Since the lawyer is on a salary, we know that the lawyer’s yearly compensation is $65,000, no matter how many hours are worked.  The paralegal is paid hourly, and the total yearly compensation will be calculated from the pay rate, normal hours worked per week, hours of overtime worked per week, and how many weeks worked in a year.

A helpful tool to calculate this is an Hourly Wage Earnings Calculator.

After we finish with the math, we learn that the paralegal earned a total of $64,750 for that year.  This is very comparable to the total salary earnings of the lawyer at $65,000.

This is only an example, but it may give some insight into what is worth more when it comes to a new job, or a career path. 

For other financial calculators that can help with money matters, follow this link: Financial Calculators.   Good Luck!

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Profit Margin vs. Profit Markup…Show Me The Money!

One of the most important factors of running a business is staying in business.  That might sound a little redundant, but I’m sure you’ve seen businesses start and businesses fail in just about any aspect of your community.  Why do so many businesses fail?  Usually it is because they spend more money than they make.  The difference between how much you spend (cost), and how much money you bring in (revenue), is profit.  And profit is the main focus on how successful a business is.

So now that we know how important profit is, we need to look at the two main ways that profit is calculated.  As stated above, profit is the difference between how much money is spent and how much is generated.  Usually profit is measured as a percentage in either Profit Margin, or Profit Markup.  

Profit Margin is calculated as the percentage of profit when compared to the total sales price.  Profit Markup is calculated as a percentage increase over the cost.

For example:  If you work at a clothing store and you have a 25% markup on a pair of jeans that has a cost of $40.00, your sales price would be $40.00 plus 25% of $40.00.  This comes out to a sales price of $50.00.

For an example of Profit Margin:  Using the same story, you have a sales price of $50.00.  Your cost is $40.00.  Your total profit is $10.00. $10.00 is 20% of $50.00.  Your margin is 20%.

Sometimes it can be confusing, but you have the same dollar amount of profit, you are just measuring it differently.

To learn more about these terms, follow the links below:

Profit Calculator                      Profit Margin                   Profit Markup

Now that you know how to calculate margin, go out there and become a captain of industry!

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

Pharaoh Wants To Know....Pyramid Math

Made famous by the ancient Pharaohs centuries ago, pyramids are shapes that have taken their place in history.  The Pyramids of Giza are one of the ancient wonders of the world.  With the centuries of time and weather, they have been proven to be some of the sturdiest man-made structures in the history of man-kind.  With all the pressures of designing one of the most important structures in human history, what kind of math did the ancient engineers need to know?

Well, perhaps they started with volume and area.

Before determining the volume or area, we first need to determine what type of pyramid we are working with.  Pyramids can have many different variations.  Usually there are two ways to classify a pyramid.  First is the base.  Many pyramids, like the Pyramids of Giza, are square base pyramids, but the base can also be a triangle, rectangle, pentagon, etc.  As long as the base has at least 3 sides, it can stand upright.  All pyramids have triangular sides that meet at a point on top.  However, a pyramid that has the top point directly over the center of the base will have equal triangular sides all around and is referred to as a “regular” pyramid.  If the top point is not over the center of the base and not all of the sides are the same, this is an “irregular” pyramid. The Pyramids of Giza are square regular pyramids with all of the triangular sides of equal shape, and the top point directly over the center of the square base.

Determining the surface area of a pyramid is fairly basic.  To determine the total surface area, you simply add the individual areas of the lateral sides and the base.  On a square regular pyramid, like the Pyramids of Giza, you would add the areas of the 4 individual triangular sides and the base.  On a regular triangular pyramid, you would add the areas of the 3 individual triangular sides with the area of the base.

To learn more about the calculation of the surface area of a regular square pyramid or a regular triangular pyramid, follow these links:

Surface Area Regular Square Pyramid               Surface Area Regular Triangular Pyramid

When the ancient engineers were thinking about how much material was needed to build the massive pyramids, they most likely needed to determine the volume.  The first step to determining the volume of a pyramid is still to identify what type of pyramid you are working with.  Once you have determined the type, find the area of the base and multiply the base area by 1/3^rd of the total pyramid height.

To learn more about the calculation of the volume of pyramids, follow this link:

Pyramid Volume Calculator

So when it’s time for you to build a new home, maybe you should look into building a pyramid.  After all, it may last longer than you.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

The Heat Index. Is it Hot Enough for Ya?

I don’t know about you, but I seem to always take a moment to look at what the weather is going to be like for the day, or week, ahead.  I have lived in some hot areas of the world and I always get a little nasty feeling whenever a meteorologist mentions the heat and dramatically throws out the calculated heat index.  As if it isn’t hot enough already, it seems like the weather folks love to point out that you’ll be even more miserable than you thought.  And if you really look into how the heat index works, you will realize that it truly is a mathematical gauge for misery.

The heat index is calculated from a mathematical formula that combines the air temperature and the amount of water in the air to determine what the outside air temperature “feels” like if it were a dry day.  This doesn’t sound very exact, but it is pretty common that people notice that they sweat more and it “feels” hotter when there is a lot of humidity in the air.  An 85 degree day (we’re working with Fahrenheit for our example) with 80% humidity is going to “feel” miserably hot compared to a 90 degree day with 0% humidity.  Or, at least to a large sampling of the population, it would be miserable.

As an example of the extreme misery that the Heat Index can bring on to us, let’s take a look at a potential real life example:

Let’s say you live in the Everglades in Florida.  It’s not unusual to have a summer day in the mid 90’s. Because it’s a swampy area, it wouldn’t be unusual to have a high humidity in the air.  If you had a day that was 95 degrees Fahrenheit and 85% humidity, the heat index would tell you that your body will feel as though it is 140 degrees outside.  That is ridiculous!  In some parts of the world the heat index can get a lot further up there.

To learn more about how the heat index is calculated, follow these links:
Heat Index Calculator (Fahrenheit)     Heat Index Calculator (Celsius)

Although we talk about the heat index with mockery and disbelief, it is an important tool when preparing for hot days.  When the heat index is high, we need to keep very close watch on our bodies for threats of dehydration, heat stroke, and fatigue.

While the heat index likes to make us miserable when it’s hot out, its cousin, the wind chill factor, is also a gauge of what the temperature “feels” like to our sensitive bodies.  Unlike the heat index, wind chill is found from an equation that considers temperature and wind speed. 

Go to the Calcunation Temperature Menu to learn more about wind chill, temperature, and heat indices.

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)