A hydraulic system operates based on Pascal's principle.
In this hydraulic system, a small force, F1 is applied to the small piston resulting in a large force , F2 at the piston K. The pressure, due to the force, F1, is transmitted by the liquid to the large piston.
Pressure, P = F1/A1
This pressure is transmitted through the liquid and acts on the base of the large piston.
Force on the large piston, F2 = P X A2 = (F1/A1) X A2.
The large force causes the load to rise.
Also F2/F1 = A2/A1
Output force / input force = output piston area / input piston area
Because of the much larger surface area, A2 of the piston K compared to the surface area, A1 of the piston, the resultant force, F1.
This shows that a large force can be produced by a small force, using Pascal's principle.
Hydraulic systems act as a force multiplier where A2/A1 is the multiplying factor.
For example, if A2=5A1, then F2 = 5F1
since F2 = F1 X (A2/A1)
A hydraulic system must not contain any air bubbles in any portion of its hydraulic fluid system.
The presence of air bubbles in the hydraulic fluid system will reduce the efficiency of the system as part of the applied force will be used to compress the air bubbles.
Wednesday 10 November 2010
Understanding Hydraulic System
Understanding Displacement, Speed and Acceleration
Distance and Displacement
Distance is the total path length traveled from one location to another. It is a scalar quantity.
Displacement is the distance between two locations measured along the shortest path connecting them, in specified location. It is a vector quantity. The SI unit of distance and displacement is metre (m).
Speed and Velocity
Speed is the distance traveled per unit time or the rate of change of distance.
Speed = total distance traveled / time taken
Velocity is the speed in a given direction or the rate of change of displacement.
Average velocity = displacement/ time taken
Acceleration and Deceleration
Acceleration is the rate of change of velocity.
Acceleration = change of velocity / time taken
Change of velocity = final velocity (v) – initial velocity (u)
Acceleration = (final velocity – initial velocity) / time taken = (v – u) / t
Things to remember:
1. Constant velocity means the object is not accelerating. Acceleration is zero.
2. Constant acceleration means the object is increasing its velocity.
Distance is the total path length traveled from one location to another. It is a scalar quantity.
Displacement is the distance between two locations measured along the shortest path connecting them, in specified location. It is a vector quantity. The SI unit of distance and displacement is metre (m).
Speed and Velocity
Speed is the distance traveled per unit time or the rate of change of distance.
Speed = total distance traveled / time taken
Velocity is the speed in a given direction or the rate of change of displacement.
Average velocity = displacement/ time taken
Acceleration and Deceleration
Acceleration is the rate of change of velocity.
Acceleration = change of velocity / time taken
Change of velocity = final velocity (v) – initial velocity (u)
Acceleration = (final velocity – initial velocity) / time taken = (v – u) / t
Things to remember:
1. Constant velocity means the object is not accelerating. Acceleration is zero.
2. Constant acceleration means the object is increasing its velocity.
Understanding Work and Energy
Work
1. Work is defined as the product of the applied force and the displacement of an object in the direction of the applied force.
2. W = F x d
3. W= work done, F = force applied, d = displacement in the direction of force.
4. SI unit for work = Joule (J), other unit = Nm
5. Work is not done when:
Energy (Energy is the capacity to do work)
1. Energy exists in different forms: kinetic energy, gravitational potential energy, elastic potential energy, sound energy, heat energy, light energy, electrical energy and chemical energy.
2. The unit for energy is Joule (J) – same as work
3. The work done is equal to the amount of energy transferred.
4. Kinetic energy is the energy of an object due to its motion.
5. Kinetic energy or work done is given by:
1. Work is defined as the product of the applied force and the displacement of an object in the direction of the applied force.
2. W = F x d
3. W= work done, F = force applied, d = displacement in the direction of force.
4. SI unit for work = Joule (J), other unit = Nm
5. Work is not done when:
- The object is stationary or not moving
- No force is applied on the object in the direction of displacement.
- The direction of motion of the object is perpendicular to that of the applied force.
Energy (Energy is the capacity to do work)
1. Energy exists in different forms: kinetic energy, gravitational potential energy, elastic potential energy, sound energy, heat energy, light energy, electrical energy and chemical energy.
2. The unit for energy is Joule (J) – same as work
3. The work done is equal to the amount of energy transferred.
4. Kinetic energy is the energy of an object due to its motion.
5. Kinetic energy or work done is given by:
- a. ½ mv2
- b. M = mass, v = velocity
- c. Unit: Joule
- E = mgh
- M = mass, g = acceleration due to gravity, h = height in metre
Understanding Scalar and Vector quantities
Scalar quantities: Quantities that have magnitude only. ( Speed, mass, distance)
Example:
For example speed has unit of ms^-1. but it has no direction.
Mass is kg but we don't know the direction.
Distance is 2km but no direction.
Vector quantities: Quantities that have magnitude and direction. (Velocity, Weight, Displacement)
Example:
Velocity unit is ms^-1 but we must state the direction that is whether from right to left.
Weight unit is Kg but the direction is towards the gravity pull of the earth.
Displacement is 2km but to the north from the point of reference.
Example:
For example speed has unit of ms^-1. but it has no direction.
Mass is kg but we don't know the direction.
Distance is 2km but no direction.
Vector quantities: Quantities that have magnitude and direction. (Velocity, Weight, Displacement)
Example:
Velocity unit is ms^-1 but we must state the direction that is whether from right to left.
Weight unit is Kg but the direction is towards the gravity pull of the earth.
Displacement is 2km but to the north from the point of reference.
Understanding Measurement
A micro balance is used to measure minute masses. It is sensitive but not very accurate.
Slide callipers are usually used to measure the internal or external diameter of an object.
A micrometer screw gauge is used to measure the diameter of a wire of the thickness of a thin object.
All measurement must consider this:
Accuracy: Ability of the instrument to measure the true value or close to the true value. The smaller the percentage error, the more accurate the instrument is.
Sensitivity of an instrument is the ability of the instrument to detect any small change in a measurement.
Consistency: ability of the instrument to produce consistent measurement.(the values are near to each other). The lower the relative deviation, the more consistent the measurement is.
How to increase accuracy?
- repeat the measurements and get the mean value.
- correcting for zero error.
- avoiding parallax error.
- use magnifying glass to aid in reading.
The sensitivity of a mercury thermometer can be increased by;
-having a bulb of thinner wall.
-having a capillary tube of smaller diameter or bore.
Slide callipers are usually used to measure the internal or external diameter of an object.
A micrometer screw gauge is used to measure the diameter of a wire of the thickness of a thin object.
All measurement must consider this:
Accuracy: Ability of the instrument to measure the true value or close to the true value. The smaller the percentage error, the more accurate the instrument is.
Sensitivity of an instrument is the ability of the instrument to detect any small change in a measurement.
Consistency: ability of the instrument to produce consistent measurement.(the values are near to each other). The lower the relative deviation, the more consistent the measurement is.
How to increase accuracy?
- repeat the measurements and get the mean value.
- correcting for zero error.
- avoiding parallax error.
- use magnifying glass to aid in reading.
The sensitivity of a mercury thermometer can be increased by;
-having a bulb of thinner wall.
-having a capillary tube of smaller diameter or bore.
Understanding Pressure
- Pressure on an area, A is the normal force, F, whish is being applied perpendicularly to the area.
- Pressure on an area, A is expressed as the normal force, F per unit area, A.
- P = (F/A)
- This SI unit for pressure is the pascal, Pa, where 1 Pa = 1 N/m2 (metre square).
- Pressure is increased: if the force, F applied to a given area, A is increased and if a given force, F is applied to a smaller area, A.
- If a balloon is pressed against by a finger, the balloon will only change its shape a bit. If the balloon is pushed against by a needle with the same force, the balloon will burst. This is because a finger has a larger surface area (A) than a needle. Hence, the needle exerts much pressure than the finger and perforates through the surface of the balloon and making a hole and freeing the air inside the balloon.
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