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  4. N° 13 Bernoulli's theorem

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Flow in a flow limiter:

just understand the

Bernoulli's theorem

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In hydraulic circuits, the same component can be called choke, flow restrictor or flow limiter.

The role of the flow limiter is to reduce the speed of the receivers (jacks or motors).

 1- Flow / speed concept

1.1 Motor loaded at 50 bars

 

Notion debit vitesse 50 bars 1

In the diagram above, a fixed displacement pump (item 1) protected by a pressure relief valve (item 2) set at 200 bars delivers 30 l / min.

The circuit directly feeds a hydraulic motor. The pressure created by the load required to run the engine is 50 bars.

The engine runs at 300 rpm, the speed created by the pump flow. There is a pressure of 50 bars on the pressure gauge M2 and a pressure of 52 bars on the pressure gauge M1. This pressure difference is due to the loss of loads. (Pressure created by the friction of the oil in the pipework).

 1.2 Motor loaded at 100 bars

 

Notion debit vitesse 100 bars 1

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In the diagram above, the same circuit with a motor forcing with a pressure of 100 bars.

It can be seen that the engine is running at the same speed (300 rpm). The pressure on the pressure gauge M2 is 100 bars and 102 bars on M1.

We can deduce that the pressure is the image of the Force and the flow rate is the image of the Speed.

2- Flow in a restrictor

2.1 Motor loaded at 50 bars

 

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Limiteur de debit theoreme bernouilli 50 bars 1

In the diagram above, a flow limiter is added to the circuit to reduce the speed of the motor.

The mechanical strength of the motor creates a pressure of 50 bars on M2. The engine runs at low speed (100rpm) since the flow limiter only allows 10l / min.

The fixed displacement pump always delivers 30l / min. 10l / min go to the motor and the excess flow (20l / min) returns to the tank by the pressure relief valve at 200 bars on M1.

There is a pressure difference ( ?P  at the terminals of the flow restrictor of 150 bars (200 bars in M1 - 50 bars in M2).

2.2 Motor loaded at 100 bars

Limiteur de debit theoreme bernouilli 100 bars 1

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The motor forces at a pressure of 100 bars read on the gauge M2.

There is a decrease in the speed of the motor at 90 rpm due to the decrease of the (ΔP) at the terminals of the flow restrictor at 100 bars (200 bars in M1 - 100 bars in M2).

The fixed displacement pump always delivers 30l / min. 7 l / min go to the hydraulic motor and the excess flow (23l / min) returns to the tank by the pressure relief valve at 200 bars read on M1.

According to Bernoulli's theorem, the flow passing through a limiter of flow varies according to the pressure difference across it.

Q = K*S* √?P

Q : flow.

K : form factor of the flow limiter.

S : passage section of the flow limiter.

2.3 Motor blocked

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Limiteur de debit theoreme bernouilli moteur bloque 1

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The motor is blocked, it does not turn anymore.

The ( ?P  across the flow restrictor is zero (200 bars in M1 - 200 bars in M2).

No flow passes through the limiter of flow and the total flow of the pump (30l / min) returns to the tank by the pressure relief valve at 200 bars in M1.

3-Conclusion

The speed of a receiver regulated by a flow limiter will not remain constant if the load (of the cylinder or motor) changes.

It will be possible to use a flow regulator which will keep a constant ?P  across its restriction and thus maintain the speeds of the receivers even if the charges change.

 

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