Types of Flow
A distinction is made between laminar and turbulent flow.
In the case of laminar flow, the hydraulic fluid moves through the pipe in ordered cylindrical layers. The inner layers of liquid move at higher speeds than the outer layers. If the flow velocity of the hydraulic fluid rises above a certain point (known as the critical speed), the fluid particles cease to move in ordered layers. The fluid particles at the centre of the pipe swing out to the side. As a result, the fluid particles affect and hinder one another, causing an eddy to be formed; flow becomes turbulent. As a consequence of this, power is withdrawn from the main flow. A method of calculating the type of flow in a smooth pipe is enabled by the Reynolds’ number (Re). This is dependent on
• the flow velocity of the liquid v (m/s)
• the pipe diameter d (m)
• and the kinetic viscosity ? (m2/s)
The physical variable “kinematic viscosity” is also referred to simply as “viscosity”.
A value for Re calculated with this formula can be interpreted as follows:
• laminar flow: Re 2300
The value 2300 is termed the critical Reynolds’ number (Recrit) for smooth round pipes.
Turbulent flow does not immediately become laminar on falling below (Recrit).
The laminar range is not reached until 1/2 (Recrit).
Measurement of Flow Rate
The simplest method of measuring flow rate is with a measuring container and a stop watch. However, turbine meters are recommended for continuous measurements. The speed indicated provides information about the value of the flow rate. Speed and flow rate behave proportionally.
Another alternative is to use an orifice. The fall in pressure recorded at the orifice is an indication of the flow rate (pressure drop and flow rate behave proportionally), measurement by orifice is scarcely influenced by the viscosity of the hydraulic fluid.
Temperature Measurement
The temperature of hydraulic fluid in hydraulic installations can either be measured using simple measuring devices (thermometers) or else by means of a measuring device which sends signals to the control section. Temperature measurement is of special significance since high temperatures (> 60 degrees) lead to premature ageing of the hydraulic fluid. In addition, the viscosity changes in accordance with the temperature.
The measuring devices may be installed in the hydraulic fluid reservoir. o keep the temperature constant, a pilotherm or thermostat is used which switches the cooling or heating system on as required.
Pressure Measurement
To measure pressures in the lines or at the inputs and outputs of components, a pressure gauge is installed in the line at the appropriate point.
A distinction is made between absolute pressure measurement where the zero point on the scale corresponds to absolute vacuum and relative pressure measurement where the zero point on the scale refers to atmospheric pressure. In the absolute system of measurement, vacuums assume values lower than 1, in the relative system of measurement, they assume values lower than 0.
Flow rate
Flow rate is the term used to describe the volume of liquid flowing through a pipe in a specific period of time. For example, approximately one minute is required to fill a 10 litre bucket from a tap. Thus, the flow rate amounts to 10 l/min.
In hydraulics, the flow rate is designated as Q. The following equation applies:
The equations for the volume (V) and the time (t) can be derived from the formula for the flow rate. The following equation is produced:
V = Q · t
Pressure transfer
The hydrostatic pressure p1 exerts a force F1 on the area A1 which is transferred via the piston rod onto the small piston. Thus, the force F1 acts on the area A2 and produces the hydrostatic pressure p2. Since piston area A2 is smaller than piston area A1, the pressure p2 is greater than the pressure p1. Here too, the following law applies:
In the case of the double-acting cylinder, excessively high pressures may be produced when the flow from the piston rod area is blocked:
Displacement transmission
If a load F2 is to be lifted a distance S2 in line with the principle described above, the piston P1 must displace a specific quantity of liquid which lifts the piston P2 by a distance S2
Displacement transmission
The necessary displacement volume is calculated as follows:
V1 = S1 · A1 and V2 = S2 · T2
Since the displacement volumes are identical (V1 = V2), the following equation is valid:
s1 · A1 = s2 · A2
From this it can be seen that the distance s1 must be greater than the distance s2 since the area A1 is smaller than the area A2.
The displacement of the piston is in inverse ratio to its area. This law can be used to calculate the values s1 and s2. For example, for s2 and A1.
Power transmission example
A vehicle is to be lifted by a hydraulic jack. The mass m amounts to 1500 kg. What force FT1T is required at the piston?
Power transmission
Power transmission
The same pressure applies at every point in a closed system. For this reason, the shape of the container has no significance.
Power transmission
Where a container is formed as shown in the diagram, it is possible to transmit forces. The fluid pressure can be described by means of the following equations:
Pressure transmission
If a force FT1T acts via an area AT1T on an enclosed liquid, a pressure p is produced which extends throughout the whole of the liquid (Pascal’s Law). The same pressure applies at every point of the closed system (see diagram).
Pressure transmission
Owing to the fact that hydraulic systems operate at very high pressures, it is possible to neglect the hydrostatic pressure (see example). Thus, when calculating the pressure in liquids, the calculations are based purely on pressure caused by external forces. Thus, the same pressure acts on the surfaces AT2T, AT3T as on AT1T. For solid bodies, this is expressed by means of the following formula:
