Chapter 3

Energy and Power in hydraulic system

Learning Objectives 1. Differentiate between hydraulic energy and hydraulic power. 2. Define the term efficiency. 3. Describe the operation of an air-to-hydraulic pressure booster. 4. Explain the conservation of energy law. 5. Calculate fluid flow rates and velocities using the continuity equation. 6. Evaluate the power delivered by a hydraulic cylinder. 7. Determine the speed of a hydraulic cylinder. 8. Describe the differences among elevation energy, pressure energy, and kinetic energy.` 9. Describe the operation of a hydraulic jack. 10. Apply Bernoulli’s equation to determine the energy transfer within a hydraulic system.` 11. Understand the meaning of the terms elevation head, pressure head, and velocity head.` 12.Differentiate between the terms pump head, motor head, and head loss.`

Block diagram of hydraulic system showing major components along with energy input and output terms. Energy is defined as the ability to perform work, Power is defined as the rate of doing work or expending energy. Input ME — Lost HE = Output ME where ME = mechanical energy, HE heat energy.

REVIEW OF MECHANICS Three laws of motion dealing with the effect a force has on a body: 1. A force is required to change the motion of a body. 2. If a body is acted on by a force, the body will have an acceleration proportional to the magnitude of the force and inverse to the mass of the body. 3. If one body exerts a force on a second body, the second body must exert an equal but opposite force on the first body.

Linear Motion linear velocity where in the English system of units: s distance (in or ft), t = time (s or mm), v = velocity (in/s, in/min, ft/s, or ft/min).

Acceleration If the body’s velocity changes, the body has an acceleration, which is defined as the change in velocity divided by the corresponding change in time where F force (lb), a acceleration (ft/s2), m mass (slugs).

Energy Let’s assume that a force acts on a body and moves the body through a specified distance in the direction of the applied force where F- force (lb), S - distance (in or ft), W - work (in . lb or ft . lb).

Power Power is a measure of how fast work is done where F force (lb), velocity (in/s, in/min, ft/s, or ft/min power has units of in lb/s, in lb/min, ft lb/s, or ft lb/min

Horsepower Power is usually measured in units of horsepower (hp). By definition, 1 hp equals 550 ft lb/s or 33,000 ft lb/mm. Thus, we have

Angular Motion Example: Force F applied to wrench creates torque T to tighten bolt. The force F creates a torque T about the center of the bolt. It is the torque T that causes the wrench to rotate the bolt through a given angle until it is tightened.

Torque T Where F- force (lb), R-moment arm (in or ft), T - torque (in . lb or ft . lb). The resulting torque causes the disk and thus the connecting shaft to rotate at some angular speed measured in units of revolutions per minute (rpm). The amount of horsepower transmitted can be found from Where T - torque (in . lb), N -rotational speed (rpm), HP - torque horsepower or brake horsepower.

Delivering power via a rotating shaft Force F applied to periphery of disk creates torque T in shaft to drive pump at rotational speed N. Q is the flow rate of oil (volume per unit time) produced by pump.

Torque horsepower and brake horsepower (BHP) The horsepower which is transmitted by torque in a rotating shaftt is called torque horsepower. It is also commonly called brake horsepower (BHP) because a prony brake is a mechanical device used to measure the amount of horsepower transmitted by a torque-driven rotating shaft.

Efficiency The efficiency of any system or component is always less than 100% and is calculated to determine power losses.

MULTIPLICATION OF FORCE Pascal’s law This law can be stated as follows: Pressure applied to a confined fluid is transmitted undiminished in all directions throughout the fluid and acts perpendicular to the surfaces in contact with the fluid.

Operation of simple hydraulic jack.

APPLICATIONS OF PASCAL’S LAW Hand-operated hydraulic jack.

CONSERVATION OF ENERGY 1. Potential energy due to elevation (EPE) The units of EPE are ft lb. 2. Potential energy due to pressure (PPE): where  is the specific weight of the fluid. PPE has units of ft lb.

Kinetic energy (KE): If the W lb of fluid is moving with a velocity v , it contains kinetic energy, which can be found using

Total energy ET

THE CONTINUITY EQUATION The continuity equation states that if no fluid is added or withdrawn from the pipeline between stations 1 and 2, then the weight flow rate at stations 1 and 2 must be equal.

Volume Flow Rate Q The volume of fluid passing a given station per unit time The continuity equation for hydraulic systems can be rewritten as follows:

HYDRAULIC POWER It is the power delivered by a hydraulic fluid to a load-driving device such as a hydraulic cylinder. HHP and OHP The horsepower delivered by the fluid to the cylinder is called hydraulic horsepower (HHP). The horsepower delivered by the cylinder to the load is called output horsepower (OHP).

1. How do we determine how large a piston diameter is required for the cylinder?

A pump receives fluid on its inlet side at about atmospheric pressure (0 psig) and discharges the fluid on the outlet side at some elevated pressure p sufficiently high to overcome the load. This pressure p acts on the area of the piston A to produce the force required to overcome the load: or The load is known from the application the maximum allowable pressure is established based on the pump design

What is the pump flow rate required to drive the cylinder through its stroke in a specified time?

The volumetric displacement VD of the hydraulic cylinder equals the fluid volume swept out by the piston traveling through its stroke S: The required pump volume flow rate Q but since VD AS, we have

Piston velocity. Q = A v the larger the piston area and velocity, the greater must be the pump flow rate.

How much hydraulic horsepower does the fluid deliver to the cylinder?

It has been established that energy equals force times distance:

Recalling that 1 hp = 550 ft . Ibis, we obtain

Conversion of power from input electrical to mechanical to hydraulic to output mechanical in a hydraulic system.

Hydraulic Horsepower in Terms of psi and gpm Units