Review and Summary

REVIEW AND SUMMARY

• In this chapter, the basics of hydraulics such as the concepts of force, pressure and head; concept and applications of Pascal's law; difference between laminar and turbulent flow; definition and significance of Reynolds number; and the concept and applications of Darcy's equation have been discussed, in detail.

• Pressure head, P = ρ g h

• If the pressure is measured with reference to the atmospheric pressure, then it is called gauge pressure. Any pressure measured above the absolute zero pressure is termed as 'absolute pressure'.

Absolute pressure = Gauge pressure + Atmospheric pressure

Vacuum pressure = Atmospheric pressure - Absolute pressure

• Work  = Force × Distance moved

• Power = Work done/Time taken

• Energy is capacity to do work.

• Torque = Force × Moment arm = F × R

• Power transmitted by a shaft, P = 2πΝΤ / 60

• Efficiency, η = Input power/ Output power

• Pascal's law: The pressure applied to a confined fluid is transmitted undiminished in all directions.

• The two important applications of Pascal's law are: 1. Bramah's hydraulic press, and 2. Air-to-hydraulic pressure booster.

• In a hydraulic press, the output force is greater than the input force, but the output movement will be lesser than the input movement.

• Reynolds number: Re = ρVD / μ = VD / v

where the notations have usual meanings.

• If Re < 2000, then the flow is laminar.

If Re > 4000, then the flow is turbulent.

If 2000 < Re < 4000, then the flow is unpredictable.

• Flow rate or discharge: 

• Continuity equation :

Q = A1 V1 = A2 V2 = Q2

• Total energy (or head) of a liquid in motion,

• Bernoulli's equation:

• Energy equation (Modified Bernoulli's equation) :

• Darcy's equation is used to calculate the head loss due friction in the pipes.

• Laminar friction factor: f = 64/Re

• Hagen-Poiseuille equation:

• Relative roughness = ε / Ꭰ

• Head loss in valves and fittings:

• At the end of the chapter, some illustrative examples are presented for better understanding of the basics.

KEY TERMS ONE SHOULD REMEMBER

Pascal's law 

Hydraulic press

Hydraulic jack

Air-to-hydraulic pressure

booster

Force

Pressure head

Pressure

Atmospheric pressure

Gauge pressure

Absolute pressure

Flow rate

Vacuum pressure

Discharge

Work

Power

Energy

Torque

Efficiency

Laminar flow

Turbulent flow

Reynolds number

Continuity equation

Fluid energy in motion

Bernoulli's equation

Energy equation

Modified Bernoulli's equation

Energy losses in pipes

Darcy's equation

Friction factor

Hagen-Poiseuille equation

Relative roughness

Moody diagram

K-factor