It is essential to be familiar with the fundamentals of hydraulics to build hydraulic systems or interpret them correctly. In this article, we will review the interrelations between the following terms and their results.

• Mass and Force
• Pressure
• Pascal’s Law
• Absolute and Actual Pressure
• Flow Rate 
• Flow Type
• Throttle and Orifice

MASS AND FORCE RELATIONSHIP

In daily life, “force” can mean many things. 

But in physics, it has a quite clear definition: It is the ability of an object to change motion. To put it differently: The effect of a force on an object causes that object to accelerate, slow down or move in a different direction. 

NOTE: Force can also change the shape of an object (deformation). This probability is usually not taken into account. 

In physics, the increase in speed, braking and change of direction are all examples of acceleration. For this reason, force is related to repulsion. So, the higher the force, the higher the acceleration that the object is subject to. Force is also related to the mass of the object on which it moves: The bigger the mass of the object, the higher the force required to accelerate the object.

This leads us to a well-known formula: Force equals mass time acceleration. 

F(force) = m(mass) x a(acceleration)

To proceed further, it is of utmost importance to know and understand the definition of gravity. If air resistance is not taken into account, we assume that all objects are attracted towards the Earth with the same acceleration. This is known as gravity or “g” in short. Gravitational acceleration is not the same everywhere in the world. However, it is 9.8 m/s² (N/kg) on average. 

When we put an object on a surface, the surface must be against the acceleration due to gravity. Gravity of the object is the force applied on the surface by the body by being multiplied by gravitational acceleration.

FG (force) = m(mass) x g(gravitational acceleration)

Figure 1 Mass

The Concept of Pressure

If we hold a contained filled with liquid and apply force to the liquid using a piston, we create hydrostatic force. Pressure is an important variable to consider when defining processes carried out with liquids.

The amount of pressure (p) in the contained liquid depends on the force (F) applied and the surface area (A) of the piston. It is independent of the amount of liquid, size or shape of the container and the type of liquid. The higher the force applied is, the higher the pressure will be. This relationship leads us to a formula to calculate static pressure: Pressure is the ratio of the force to the area.

F (force) = P(pressure) x A(surface area)

                                                                                  Figure 2 The Concept of Pressure

1 psi = 6.9 Pa 
1 bar = 14.5 psi
1 bar = 100 Pa

Pascal’s Law

Liquids and solid objects transfer force differently. The following example shows a load placed on a fixed installation. If we place the load on the moving lid of a container filled with liquid, gravity will affect the liquid, creating pressure in it. 

The pressure created not only moves downwards but it equally spreads in all directions throughout the liquid. Pressure always moves vertically to the walls of the container. Value of the pressure (p) in the liquid equals force (F) divided by area (A). The pressure is equal anywhere in the liquid. (Pascal’s Law)

Figure 3 Pascal’s Law

Figure 4 Force Transmission

P1 = P2

F1/A1 = F2/A2

As pressure will spread equally on all surfaces, it is applied evenly on all surfaces regardless of the shape of the container.

V1 = V2

s1.A1 = s2.A2

Figure 5

F1 = F2

P1 x A1 = P2 x A2

The concept of absolute and actual pressure

Considering the following example, let us assume that the value read on the gauge is -3 psi.  We should remember that in such a system, absolute pressure would be 11.5 psi. 

Pabs = Pman + 14,5 psi (atm pressure)

Figure 6 Absolute & Gauge Pressure

FLOW RATE

Another physical variable required to better understand hydraulic systems is the flow rate.

Flow rate shows how much liquid flows through a system in a certain period of time.

qv (flow rate) = V (volume) / t (time)

For cylindrical structures,

qv (flow rate) = V (speed-cm/s) * A (area-cm2) * 0.06

This formula can be used.

Figure 7 Change of flow according to different sections

Flow speed or rate does not change according to varying sections

    Qv1 (flow rate) = V1 (speed-cm/s) * A1 (area-cm2) * 0.06

    Qv2 (flow rate) = V2(speed-cm/s) * A2 (area-cm2) * 0,06

As the flow rate does not change,

V2 (speed-cm/s) / A1 (area-cm2) = V1 (speed-cm/s) / A2 (area-cm2) 

flow type

Flow type is another variable of particular importance. The type may vary depending on the fluid rate. There are two types of flow: Laminar and turbulent.

Fluids moving at lower speeds have laminar flow characteristics, meaning the fluid flows through the pipe in layers. While the inner fluid layer moves at the highest speed, the outmost layer that contacts the walls of the pipe has almost nearly zero speed and is almost stable. There is no mixing between the walls and there are no vortexes or cross flows. This kind of flow only causes minimum energy and pressure loss.

If the flow rate is increased to a critical point, nature of the flow will start to change. Vortexes will form in the flow, which may cause the flow lines to get mixed completely. This is known as turbulent flow. Turbulent flow causes increased flow resistance and as a result, increased hydraulic losses.

Figure 8 Laminar and Turbulent Flow

Transition from laminar to turbulent flow generally causes big losses of pressure. For this reason, turbulent flow is something to avoid in hydraulics under normal circumstances.

The type of flow to occur in circular straight tube can be determined mathematically according to the flow rate. The “Reynolds number” is referred to do this. 

The Reynolds number equals the flow rate times of the tube’s inner diameter divided by the kinematic viscosity of the fluid. It is a number without a unit.  For transition between laminar and turbulent flow, the threshold or critical value is set to 2,300 approximately. A Reynolds number below the critical value indicates laminar flow, while number above the critical value indicates turbulent flow.

Re = v (flow are-cm/s) * d (inner diameter-cm) / v ( kinematic viscosity cm2/s )

Type of flow is determined according to the value of the Reynold number.

Re < 2300  Laminar

Re > 2300  Turbulent

The concept of throttle and orifice

Hydraulic throttle valves or orifices can be adapted to hydraulic systems to adjust the flow rate. When selecting these two products, it is important to decide the intended use and application. As the throttle way (I) is longer in standard throttle ways compared to orifices, it may affect the viscosity of the hydraulic fluid. Such problem does not occur in orifices.