CE Lecture 2a

7/24/2019 CE Lecture 2a

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Prepared By: MUHAMMAD MOEEN SULTAN Department of Mechanical Engineering UET Lahore, KSK Campus

CONTROL ENGINEERINGLecture 2


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Hydraulic Resistance

It is the resistance to flow which occurs as a result of aliquid flowing through valves or changes in a pipe

diameter as shown in Figure.

The relationship between the change in flow rate of liquidq through the resistance element and the resulting

pressure difference (p1p2) is given as

Fluid Systems


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Hydraulic Resistance

Pressure drop p1- p2 is equivalent to voltage drop andflow rate qto current, Ris equivalent to electrical

resistance.

Fluid Systems


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Hydraulic Capacitance

It is the term used to describe energy storage with a liquidwhere it is stored in the form of potential energy as shown

in Figure. A height of liquid in the container shown (called

pressure head) is one form of such storage.

Fluid Systems


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The rate of change of volume Vin the tank (dV/dt) isequal to the difference between the volumetric rate at

which liquid enters the container q1 and the rate at which

it leaves the container q2

But V =Ah, whereAis the cross-sectional area of thecontainer and his the height of liquid in it. Hence

Fluid Systems


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The pressure difference between the input and output isp, wherep = hg with being the liquid density and gthe

acceleration due to gravity.

The hydraulic capacitance C is defined as

Fluid Systems


7/34Prepared By: MUHAMMAD MOEEN SULTAN Department of Mechanical Engineering UET Lahore, KSK Campus

Therefore,

Integration of above equation gives

Fluid Systems



Hydraulic Inertance

It is the equivalent of inductance in electrical systems or aspring in mechanical systems. To accelerate a fluid and to

increase its velocity a force is required.

Fluid Systems



Consider a block of liquid of mass mas shown in Figure.The net force acting on the liquid is

Where (p1p2) is the pressure difference andAthecross-sectional area. This net force causes the mass toaccelerate with an acceleration a, and so

However, ais the rate of change of velocity dv/dt,therefore

Fluid Systems

A



The mass of liquid concerned has a volume ofAL, whereLis the length of the block or the distance between the

points in the liquid where the pressuresp1andp2are

measured. If the liquid has a density then m = AL, and

But the volume rate of flow q = Av, hence

Fluid Systems



Fluid Systems

1



Example 1

Figure shows a simple hydraulic system as the liquidenters and leaves a container. Such system can be

considered to consist of a capacitor, the liquid in the

container, with a resistor, the valve. Inertance may be

neglected since flow rates change only very slow.

Modeling Hydraulic System


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For the capacitor we can write

Integration of Equation gives



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The rate at which liquid leaves the container q2 equalsthe rate at which it leaves the valve. Therefore for the

resistance R we have

The pressure difference (p1p2) is the pressure due tothe height of liquid in the container and is thus hg with

being the liquid density and g the acceleration due to

gravity. Therefore



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Similarly, we may define the capacitance, C, of a tank tobe the change in quantity of stored liquid necessary to

cause a unit change in potential, and so substituting for

q2 in previous Equation gives

And, since C = A/g



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Example 2



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The commonality of systems from the various disciplinesby demonstrating that the mechanical systems with which

we worked can be represented by equivalent electric

circuit.

An electrical circuit that is analogous to a system fromanother discipline is called an electrical circuit analog.

Analogs can be obtained by comparing the describingequations, such as the equations of motion of a

mechanical system, with either electrical mesh or nodalequations.

Electrical Circuit Analogs


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When compared with mesh equations, the resultingelectrical circuit is called a series analog.

When compared with nodal equations, the resultingelectrical circuit is called a parallel analog.

Electrical Circuit Analogs


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Series Analog


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Series Analog


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Series Analog


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Series Analog


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Series Analog


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Series Analog


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Series Analog


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Kirchoffsnodal equation for the simple parallel RLCnetwork shown in figure is

Parallel Analog


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Parallel Analog


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Parallel Analog


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Parallel Analog


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Parallel Analog


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Parallel Analog


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Parallel Analog

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CE Lecture 2a