PASCAL

• Pressure in an enclosed fluid can be considered uniform

throughout a practical system.

• Small differences may arise from head pressures at

different heights, but negligible compared with the system

operating pressure.

Pascal’s Law

• Pascal's law AKA Principle of transmission of fluid-

pressure

• is a principle in fluid mechanics that states that pressure

applied anywhere in a confined incompressible fluid is

transmitted equally in all directions

If F at A is 50 lbf, how much the pressure at B,C,D & E?

A) PA = PB = PC = PD = PE

B) PA = PB+PC+PD+PE

• Hydraulic and pneumatic systems are concerned with the flow of fluid down a pipe.

• Velocity flow of a system measures linear speed past a point of measurement.

Flow rate

• Laminar flow:

1) Low flow velocity

2) Flow pattern is smooth

3) Low velocities at the pipe walls

4) Highest flow at the center of pipe

Types of fluid flow

• Laminar flow

• Re < 2000

• 'low' velocity

• Dye does not mix with water

• Fluid particles move in straight lines

• Rare in practice in water systems.

• Turbulence:

1) Particle do not move parallel

2) Become turbulent when velocity increased

3) Sudden change in direction of cross section

Types of fluid flow

• Turbulent flow

• Re > 4000

• 'high' velocity

• Dye mixes rapidly and completely

• Particle paths completely irregular

• Average motion is in the direction of the flow

• Cannot be seen by the naked eye

• Changes/fluctuations are very difficult to detect. Must use laser.

• Mathematical analysis very difficult - so experimental measures

are used

• Most common type of flow

• The nature of flow is determined by Reynolds number (Rc),

Rc = (vdρ)/η where v : flow velocity (m/s) d : pipe diameter (m) ρ : fluid density (kg/m3) η : dynamic viscosity of fluid (kg/(m.s))

• If Rc < 2300, flow is laminar. If Rc > 4000, flow is

turbulent

Types of fluid flow

• Kinematic viscosity, k = η/ρ • Replacing k into Rc Rc = (vd)/k where v : flow velocity (m/s) d : pipe diameter (m) k : kinematic viscosity of fluid (m2/s)

• If Rc < 2300, flow is laminar. If Rc > 4000, flow is

turbulent

Reynolds number

k : fluid kinematic viscosity

• The SI unit of kinematic viscosity : m2/s.

• The cgs physical unit for kinematic viscosity is the stokes

(St), named after George Gabriel Stokes. It is sometimes

expressed in terms of centistokes (cSt).

• 1 St = 1 cm2·s−1 = 10−4 m2·s−1.

• 1 cSt = 1 mm2·s−1 = 10−6m2·s−1.

• So which one is preferred in hydraulics system??

• Laminar or turbulence?

• Consideration?

• Velocity,

• smoothness of movement

• Accuracy of cylinder

• system efficiency (minimum friction loss)

• If the flow rate in a system is constant, then the total energy in the system will also be constant irrespective of the variation in the cross section of the fluid passage.

TOTAL ENERGY = POTENTIAL ENERGY + KINETIC ENERGY

Bernoulli’s Principle

where,

P1, v1 and z1 are pressure, velocity and datum height of the center line of pipe at point 1 respectively.

P2, v2 and z2 are pressure, velocity and datum height of the center line of pipe at point 2 respectively.

Bernoulli’s Equation

2

2

221

2

11

22zg

vPzg

vP

P1 P2

Point 1 Point 2

• In practice, we need to add friction head (hf), i.e. pressure lost due to friction.

• Most manufacturers specify maximum flow rate allowed through a valve.

• Valve should offer least amount of pressure drop.

• Bernoulli’s principle can guide designer of valve and pipe to use optimum size.

Bernoulli’s Equation

fhzg

v

g

P

zg

v

g

P

2

2

22

1

2

11

22

Pressure measurement

• Bourdon pressure gauge

• consists of a flattened C shaped tube which is fixed at one end.

When pressure is applied to the tube it tends to straighten, with the

free end moving up and to the right.

• For low pressure ranges a spiral tube is used to increase the

sensitivity.

• If an electrical output signal is

required, the pointer is replaced by a

potentiometer

Flow measurement

• Venturi meter

Flow measurement

• Orifice plate meter