Exp No 1, Pascal\'s law PDF

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Verification of Pascal’s la

Department of Mechanical E University Of Sharja

Student Manual

Verification of Pascal’s law

1 Fluids Mechanics Laboratory Student Manual

Verification of Pascal’s law

2 Fluids Mechanics Laboratory Student Manual

Verification of Pascal’s law

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Verification of Pascal’s law Symbols Used

Laboratory Teaching Exercises

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Verification of Pascal’s law Objective: The objective is to illustrate how liquid can be used to transmit a force. And, to investigate the relationships between the forces on the plungers, the cross section area of the plungers and the fluid pressure in the system. Also this experiment verified the Pascal’s law which is the principle of transmission of fluid-pressure is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure variations (initial differences) remain the same.

Exercise A - Observe how liquid is used to transmit force. Exercise B - Investigate the relationships between the force on the plungers, the cross section of the plungers and the fluid pressure in the system.

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Verification of Pascal’s law Safety Considerations

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Verification of Pascal’s law Intended conditions of use

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Verification of Pascal’s law

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Verification of Pascal’s law Required Personal Protective Equipmemts

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Verification of Pascal’s law General Overview The Sanderson Hydraulic System is a simple piece of apparatus designed specifically for Motor Vehicle and Mechanical Engineering Technician Courses. It is intended for use in either the classroom or laboratory and may be used for simple demonstrations to illustrate how liquid can be used to transmit a force. The apparatus may also be used by the student to carry out simple experiments to investigate the relationships between the force on the plungers, the cross section area of the plungers and the fluid pressure in the system. Apparatus Description

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Verification of Pascal’s law 1. Plunger A 2. Plunger B 3. Plunger C 4. Gauge 5. Pipe 6. Mass 7. Frame Schematic Diagram:

Technical Parameters and Dimensions

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Verification of Pascal’s law

Equipment Specifications The system consists essentially of three accurately machined cylinders and plungers whose cross-section areas are in the ration 1,2 and 6. The three cylinders and the pressure gauge are connected in parallel and "on/off" taps are included in the circuit so that any of the cylinder units may be isolated from the system. A clear Perspex oil reservoir is fitted to the "master" cylinder. Two special load hangers are provided. Overall Dimensions 9.1 Height - 0.68 m Width - 0.38 m Depth - 0.28 m Net Weight – 11 kg Environmental Conditions 9.2 This equipment has been designed for operation in the following environmental conditions. Operation outside of these conditions may result reduced performance, damage to the equipment or hazard to the operator. a. Indoor use; 12 Fluids Mechanics Laboratory Student Manual

Verification of Pascal’s law b. Altitude up to 2000 m; c. Temperature 5 °C to 40 °C; d. Maximum relative humidity 80 % for temperatures up to 31 °C, decreasing linearly to 50 % relative humidity at 40 °C; e. Mains supply voltage fluctuations up to ±10% of the nominal voltage; f. Transient over-voltages typically present on the MAINS supply; Note: The normal level of transient over-voltages is impulse withstand (overvoltage) category II of IEC 60364-4-443; g. Pollution degree 2. Normally only nonconductive pollution occurs. Temporary conductivity caused by condensation is to be expected. Theory The hydrostatic equation shows that at the same elevation in a fluid at rest the pressures are equal. This unit demonstrates Pascal's Principle, where "pressure applied to a confined fluid causes the pressure throughout the fluid at the same elevation to be increased by the same amount". Hence, by applying a small amount of force to a small-area plunger a large area plunger will exhibit a large force. The formulas that relate to this are show below: P1=P2 (as pressure is equal throughout the system)

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Verification of Pascal’s law

Since a fluid offers no permanent resistance to shear force it follows that the force exerted by a fluid is always normal to the containing surface. Let p = Intensity of fluid pressure in the container A = Cross sectional area of the cylinder F = Force acting on the plunger Neglecting friction between the cylinder and the plunger then for equilibrium of the plunger: F = pA or p = F/A

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Verification of Pascal’s law

Therefore

If A2 > A1 then there is a mechanical advantage in which the hydraulic system will be used. The experiments which may be carried out consist of investigations into the relationship between the force applied to the plunger, the cross sectional area of the plunger and the fluid pressure in the system. The gravitational force acting on the masses attached to the special load hanger provides the means of applying a force to the plunger. The ON/OFF taps may be used to isolate any of the plunger units from the system. Note: Before carrying out any experiment ensure that there is sufficient oil in the ‘Master Cylinder’ reservoir and that the system is free from air. (Bleed screws are provided should it be necessary to bleed the system.)

When the system has been bled unscrew the pressure gauge and pour oil into the gauge to fill it as much as possible. Press down on the right hand (master) plunger until oil emerges from the pressure gauge connection with no air bubbles then refit the pressure gauge using PTFE tape to seal the thread.

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Verification of Pascal’s law Before carrying out force ratio experiments using two plunger units it will be necessary to balance the forces, due to the weight of the plungers and load hangers, by attaching suitable masses to one of the hangers.

Experimental Procedure 1- Check for all the plungers that there is no air bubble or bleed it using the bleed screws 2- Check for the oil between the plungers and the gauge and fill it as much as we can. 3- Put the known weights on the hanger and note the total weight including the weight of the hanger. 4- Open the valve so the plungers can move freely. 5- After stability take the reading from the pressure gauge. 6- Then repeat these steps for other weights to take other readings for the same plunger. 7- After finishing from this plunger move to the other one and repeat these steps with using different weights also for each trial.

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Verification of Pascal’s law

Observations Table: Experiment No 1 Plunger A (Cross sectional area 1800 mm2) Obs No

Load on

Total load

Total Force

Equivalent

Gauge

% error

hanger (w)

W= w +

FA = W x

Pressure

Reading

(P- Pg)/ P x

Kg

0.573+0.198 Kg

9.81 Newton

(P= FA/ AA) Pascal

(Pg) Bar

100 %

1 2 3 4 Plunger B (Cross sectional area 600 mm2) Obs No

Load on

Total load

Total Force

Equivalent

Gauge

% error

hanger (w)

W= w +

FB = W x

Pressure

Reading

(P- Pg)/ P x

0.327+0.198 Kg

9.81 Newton

(P= FB/ AB) Pascal

(Pg) Bar

100 %

Total load

Total Force

Equivalent

Gauge

% error

Kg 1 2 3 4 Plunger C (Cross sectional area 300 mm2) Obs No

Load on

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Verification of Pascal’s law hanger (w)

W= w +

Fc = W x

Pressure

Reading

(P- Pg)/ P x

Kg

0.221+0.198 Kg

9.81 Newton

(P= Fc/ Ac) Pascal

(Pg) Bar

100 %

1 2 3 4

Specimen Graphs

Graph No 1: Pressure ~ Force on Plunger

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Verification of Pascal’s law

Graph No 2: Force on Plunger 1 ~ Force on Plunger 2 Additional graphs between Gauge pressure against force applied Gauge pressure against Percentage error

 

In conclusion, the outcomes of this experiment are to: 

Observe how liquid is used to transmit force.

 Investigate the relationships between the force on the plungers, the cross section of the plungers and the fluid pressure in the system. Typical Points for discussion  Pascal’s Law and its limitations  Practical applications of Pascal’s law  Effect of nature of working fluid 19 Fluids Mechanics Laboratory Student Manual

Verification of Pascal’s law

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