Fluid Power

ENGR 8-4, Lesson 4Using Mathematics in Fluid

PowerWritten by Roland Williams

Big Idea ENGR-TS-3: The students will

develop an understanding of how humans interact with systems.

Critical Knowledge/Elements

a) Operate technological systems

b) Maintain technological systems

c) Constructing technological systems

d) Design technological systems

Essential Question

How are mathematics used to evaluate fluid power systems?

Word Wall Fluid Fluid Power Hydraulic

Systems Pneumatic

Systems Boyle’s Law

Pascal’s Principle Pressure Actuators Compressor Mechanical

Advantage

Earlier, we learned that an actuator is a device that converts fluid power into mechanical force and motion.

The Piston is a round plunger inside of an actuator that transmits force to the fluid or transmits the force of the fluid to an object.

To find the pressure of the fluid inside of a mechanical device, we must know the area of the piston. This is done by using the formula used to determine the area of a circle.

Area of a Circle

If we know the radius:

A = r2

If we know the diameter, we must divide the diameter by 2.

If the diameter of a piston is 1 inch, we would do the following:

diameter 1” ÷ 2 = .5 radius

A = r2

A = 3.14 x .25

A = .785 square inches

Recall from the earlier lesson that the foundation of modern hydraulics was established when Pascal discovered that pressure in a fluid acts equally in all directions. This pressure acts at right angles to the containing surfaces.

Pascal’s Law

Pressure

In the last lesson, we learned that pressure is the amount of force distributed over a unit of area, usually expressed in pounds per square inch. And the formula to find pressure was:Pressure = Force (F)

Area (A)

Earlier we determined the area of the piston was .785 square inches.

To find the pressure we would:

P = F P = 50 lbsA .785 in2

P = 63.69 pounds per square inch (psi)

50 lbs of force63.69 psi

Mechanical Advantage

In the previous lesson, we learned that mechanical advantage was the increase in force gained by using a machine.

Using mathematics we can evaluate the amount of mechanical advantage we would gain by using a fluid power system.

Mechanical Advantage1 inch diameter50 lbs force

10 inches diameter5000 lbs force

63.69 PSI

If we know the PSI and Area, we can find the Force to determine mechanical advantage: F = P x A

Mathematic Worksheet

Now let’s see if you can apply you mathematics skills to fluid power systems.

Complete the Mathematics Worksheet.

Mathematic Worksheet

Let’s see how well you did on the Mathematics Worksheet.

Essential Question

How are mathematics used to evaluate fluid power systems?

Fluid Power (conclusion)

ENGR 8-4, Lesson 1Introduction to Fluid Power