Pascal's law states that pressure applied anywhere in an enclosed incompressible fluid is transmitted equally in all directions. Reynolds number determines the type of fluid flow as either laminar or turbulent based on flow velocity, pipe diameter, fluid density, and dynamic viscosity. Bernoulli's principle states that the total energy in a fluid system is constant, relating pressure, velocity, and height according to Bernoulli's equation.

1. PASCAL

2. • 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

3. • 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

4. 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

5. • 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

6. • 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

7. • Laminar flow
• Re < 2000
• 'low' velocity
• Dye does not mix with water
• Fluid particles move in straight lines
• Rare in practice in water systems.

8. • 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

9. • 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

10. • 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

11. • 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

12. 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.

13. • So which one is preferred in hydraulics system??
• Laminar or turbulence?
• Consideration?
• Velocity,
• smoothness of movement
• Accuracy of cylinder
• system efficiency (minimum friction loss)

14. • 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

15. 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
22
1
2
11
22
zg
vP
zg
vP


P1 P2
Point 1
Point 2

16. • 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 

17. 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

18. Flow measurement
• Venturi meter

19. Flow measurement
• Orifice plate meter