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Fundamentals of Fluid MechanicsProf. Charlton S. InaoDefence University College of Engineering

PE-3231Week 1Hydraulic and Pneumatic System DesignFluid powerWhat is fluid power?Fluid power is a term describing hydraulics and pneumatics technologies. Both technologies use a fluid (liquid or gas) to transmit power from one location to another. With hydraulics, the fluid is a liquid (usually oil), whereas pneumatics uses a gas (usually compressed air). 2Both are forms of power transmission, which is the technology of converting power to a more useable form and distributing it to where it is needed. The common methods of power transmission are electrical, mechanical, and fluid power.Although they sometimes are viewed as competing technologies, no single method of power transmission is the best choice for all applications. In fact, most applications are served by a combination of technologies. However, fluid power offers important advantages over the other technologies.3Fluid power systems easily produce linear motion using hydraulic or pneumatic cylinders, whereas electrical and mechanical methods usually must use a mechanical device to convert rotational motion to linear. 4Fluid power systems generally can transmit equivalent power within a much smaller space than mechanical or electrical drives can, especially when extremely high force or torque is required.

5Fluid power systems also offer simple and effective control of direction, speed, force, and torque using simple control valves. Fluid power systems often do not require electrical power, which eliminates the risk of electrical shock, sparks, fire, and explosions. What is Hydraulics?6Study of liquids at rest and in motion, specially under pressure, and application of that knowledge in design and control of machines.

In comparison, pneumatics is concerned with gases and their behavior under pressure7The word hydraulics is based on the Greekword for water, and originally covered the study of the physical behavior of water at rest and in motion. Use has broadened its meaning to include the behavior of all liquids, although it is primarily concerned with the motion of liquids.

Hydraulics includes the manner in whichliquids act in tanks and pipes, deals with their properties, and explores ways to take advantageof these properties.8Hydraulics are used for the generation, control, and transmission of power by the use of pressurized liquids.

Hydraulic topics range through some part of science and most of engineering modules, and cover concepts such as pipe flow, dam design, fluidics and fluid control circuitry, pumps, turbines, hydropower, computational fluid dynamics, flow measurement, river channel behavior and erosion.FundamentalsPneumaticHydraulicCompressed Air Industrial OilLight loads,6-8 barsHeavy loads, unlimited, no OLFast, erraticSlow, stableCompressorPumpCompressible IncompressibleAir Receiver/Air ReservoirTankExhaust to AtmosphereLiquid back to TankPU tubesHi pressure Wire braided hose10

Hydraulic System

Hydraulic System

Hydraulic System

Hydraulic Reservoir

Filter Location in hydraulics

Physical Properties of Hydraulic FluidsHydraulic fluid(s), also called hydraulic liquid(s), are the medium by which power is transferred in hydraulic machinery. Common hydraulic fluids are based on waste, mineral oil or water. Hydraulic systems like the ones mentioned above will work most efficiently if the hydraulic fluid used has zero compressibility.

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Major functions of a hydraulic fluid and the properties of a fluid that affect its ability to perform that function

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Most important three physical properties of Fluids

18Density can be considered constant.

2. Viscosity of fluids varies markedly with temperature and to a much lesser degree with pressure.

3. Bulk modulus essentially depends on pressure, entrained air and mechanicalcompliance. 19

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Distribution and Flow in Pipes21Fluid flow10/21/2015Hydraulic and Pneumatic Systems22Flow is a loose term that generally has three distinct meanings:volumetric flow is used to measure volume of fluid passing a point per unit of time. Where the fluid is a compressible gas, temperature and pressure must be specified or flow normalised to some standard temperature and pressuremass flow measures the mass of fluid passing the point in unit timevelocity of flow measures linear speed (in m s -1, say) past the point of measurement. Flow velocity is of prime importance in the design of hydraulic and pneumatic systems.22Laminar and turbulent flow10/21/2015Hydraulic and Pneumatic Systems23

The nature of the flow is determined by the Reynolds number, R c, given by the expression:

23Flow through pipes10/21/2015Hydraulic and Pneumatic Systems24

Volume flow rate is Q=vAMass flow rate is Qm=vAWhere v is average velocity24Where v is average velocityPressure and Force.10/21/2015Hydraulic and Pneumatic Systems25Pressure is force exerted against a specific area (force per unit area)An example of pressure is the air (gas) that fills an automobile tire.Force is anything that tends to produce or modify (push or pull) motion and is expressed in Newton. F = PAPressure =Force/Area; N/m2Power=Work/time=Nm/sWork =Force X distance travelled=NmFlow rate= Area x velocity; Q=AV=m2.m/sPower= Pressure x Flow Rate=N/m2x m3/s=J/s=WTorque= Force x radius=NmBasic Formula

Units of PressurePascal's Law.10/21/2015Hydraulic and Pneumatic Systems28Blaise Pascal formulated the basic law of hydraulics in the mid 17th century.He discovered that pressure exerted on a fluid acts equally in all directions. His law states that pressure in a confined fluid is transmitted undiminished in every direction and acts with equal force on equal areas and at right angles to a container's walls.It is known for Equilibrium and force amplification as long as the distance or lever arm is enough ( from the small diameter pipe /tube but with long lever arm) to equate the WORK from bigger diameter but small distance on the other side of the system.Basic Physical Laws

10/21/2015Hydraulic and Pneumatic Systems29Pressure EquilibriumForce -Area-Distance Area relationshipWork =Fd1lb x 10 in=10lbs x inchPressure Equilibrium1 lb/1 sq in.=10 lbs/10 sq in.Pascals Law=Force multiplication with constant pressure

P=37500 kgf/15,000 cm2=2.5kg/cm2250 kg/ 100 cm2=2.5 kg/cm2P=5kg/2 cm2=2.5 kg/cm2F=2.50 kgf x 15000 cm2=37,500 kgfPressure is uniform=2.5kgf/cm2Force Progress5kg25037,500 kgfPascals LawPf = P0 + ghWhen there is an increase in pressure at any point in a confined fluid, there is an equal increase at every point in the container.In a fluid, all points at the same depth must be at the same pressure.Consider a fluid in equilibrium.

PA - Ahg P0A = 0P = P0 + ghHydraulicsPressure is equal at the bottom of both containers (because its the same depth!)P = F2/A2 = F1/A1 and since A1 < A2, F2 > F1 There is a magnification of force, just like a lever, but work stays the same! (conservation of energy). W = F1* D1 = F2 * D2 D1 > D2

You have to push down the piston on the left far down to achieve some change in the height of the piston on the right.Pascal,s LawBernoullis Equation(Continuity Equation)Bernoullis equation is an equation used to determine the head of the fluid.Energy Entering the system = energy Leaving the system + EnergyLossEf=flow energy of mass entering the systemP =potential energyK= kinetic energy of mass entering the system10/21/2015Hydraulic and Pneumatic Systems33Law of conservation of mass/EnergyEf1 + P1+K1=Ef2 + P2 + K2Bernoullis equation for an Ideal systemNeglecting friction, the total head or the total amount of energy per unit mass or weight is the same at every point in the path of flowWith continuous steady flow, the total head at any point in the stream is equal to the total head at any downstream point plus the head loss between two points..10/21/2015Hydraulic and Pneumatic Systems34Bernoullis equation if friction is consideredDerivation of Bernoullis Equation

Consider the change in total energy of the fluid as it moves from the inlet to the outlet. Etotal = Wdone on fluid - Wdone by fluid Etotal = (1/2mv22 + mgh1) (1/2mv12 + mgh2)Wdone on fluid - Wdone by fluid = (1/2mv22 + mgh1) (1/2mv12 + mgh2)P2V2 - P1V1 = (1/2mv22 + mgh1) (1/2mv12 + mgh2) P2 P1 = (1/2 v12 + gh1) (1/2 v12 + gh1)

Etotal = 1/2mv2 + mgh W = F/A*A*d = PVP2 + 1/2 v12 + gh1 = P1 + 1/2 v12 + gh1 Venturi TubeA2 < A1 ; V2 > V1According to Bernoullis Law, pressure at A2 is lower.Choked flow: Because pressure cannot be negative, total flow rate will be limited. This is useful in controlling fluid velocity.

P2 + 1/2 v12 = P1 + 1/2 v12 ; P = /2*(v22 v12)Daniel BernoulliA Swiss scientist born in 1700s that is most famous for his work in fluid pressure. He died in 1782.

BERNOULLIS THEOREMBernoullis theorem which is also known as Bernoullis principle, states that an increase in the speed of moving air or a flowing fluid is accompanied by a decrease in the air or fluidspressure or sum of the kinetic (velocity head), pressure(static head) and Potential energy energy of the fluid at any point remains constant, provided that the flow is steady, irrotational, and frictionless and the fluid is incompressible.

BERNOULLIS EQUATION

If a section of pipe is as shown above, then Bernoullis Equation can be written as;39BERNOULLIS EQUATIONWhere (in SI units)

P= static pressure of fluid at the cross section;= density of the flowing fluid in;g= acceleration due to gravity;v= mean velocity of fluid flow at the cross section in;h= elevation head of the center of the cross section with respect to a datum.

HOW TO VERIFY?The converging-diverging nozzle apparatus (Venturi meter) is used toshow the validity of Bernoullis Equation. The data taken will show the presence of fluid energy losses, often attributed to friction and the turbulence and eddy currents associated with a separation of flow from the conduit walls.

APPARATUSES USEDArrangement of Venturi meter apparatus(fig.1)Hydraulic bench(fig. 2). Stop watch(fig.3).

fig. 2fig. 3PROCEDURENote down the inlet, throat and outlet section areas.Measure the distances of inlet, throat ant outlet section from origin.Switch on the motor attached to hydraulic bench.If there any water bubble is present in tube remove it by using air bleed screw. Fully open the control valve.Note down the reading of piezometer corresponding to the section, simultaneously note down the time required to a constant rise of water in volumetric tank(say of 10).Varying the discharge and take at least six readings.

OBSERVATIONSVolume = 1000 cm3Distance of inlet section from origin= 5.5 cmDistance of throat section from origin= 8.1 cmDistance of outlet section from origin= 15.6 cmArea of inlet section= 4.22 cm2Area of throat section= 2.01 cm2Area of outlet section= 4.34 cm2

OBSERVATIONSS NO.TIME(sec)PIEZOMETRIC HEAD(cm)INLETSECTIONTHROATSECTIONOUTLETSECTION190.4019.817.519.3292.9019.917.319.23101.2619.417.418.84106.0019.417.418.85110.0019.617.619.06115.6519.217.618.8CALCULATED VALUESQ(cm3/s)VELOCITY(v) (cm/sec)VELOCITY HEAD (cm)TOTAL ENERGY HEAD (cm)LOSS OF ENERGY(cm)v1v2v3v12/2gv22/2gv32/2gE1E2E3E1-E2E1-E3110.6226.255.025.40.351.540.3120.119.019.61.100.51107.6425.553.524.80.331.460.3120.218.719.51.470.7198.7623.449.122.70.271.230.2619.618.619.01.040.6194.3422.346.921.70.251.120.2419.618.519.01.130.6190.9121.545.220.90.231.040.2219.818.619.21.190.6186.4720.443.019.90.210.940.2019.418.519.00.870.41RESULTSIt is observed from the calculated value that at section where area is less velocity is high and pressure is low which validates the Bernoullis Equation. Graphs are plotted between distance v/s piezometric head and distance v/s total energy but from the graph (B) we can observe that there is dissipation in energy at last point this is because to achieve an ideal condition practically is not possible. APPLICATIONS The Bernoullis equation forms the basis for solving a wide variety of fluid flow problems such as jets issuing from an orifice, jet trajectory flow under a gate and over a weir, flow metering by obstruction meters, flow around submerged objects, flows associated with pumps and turbines etc.Apart from this Bernoullis equation is very useful in demonstration of various aerodynamic properties like Drag and Lift.APPLICATIONSDRAG AND LIFT

Fast Moving Air; Low Air PressureAir travels farther Slow Moving Air; High Air PressureairfoilLeading edgeTrailing edgeAPPLICATIONS

SummaryBernoullis equation is valid for flow as it obeys the equation.As the area decreases at a section (throat section) velocity increases, and the pressure decreases.

Velocity becomes high but the pressure drops a the throat.