FLUID MECHANICS – 1 First Semester 2011 - 2012 Week – 1 Class – 2 Pressure and Manometers Compiled and modified by Sharma, Adam
Review Introduction to Fluid mechanics Concepts and definitions Applications of fluid mechanics Dimensions and Units Basic dimensions in FM Different units of measurement Properties of fluids Density and Relative density Absolute and kinematic viscosity 2
OBJECTIVES• Concept of pressure• Pressure variation in a fluid at rest• Pressure measuring devices• Measurement of pressure using various kinds of manometers 3
PRESSUREPressure: A normal force exertedby a fluid per unit area The normal stress (or “pressure”) on the feet of a chubby person is much Some basic greater than on the feet of a slim pressure person. gages. 4
Absolute pressure: The actual pressure at a given position. It is measured relative to absolute vacuum (i.e., absolute zero pressure).Gage pressure: The difference between the absolute pressure and the local atmospheric pressure. Most pressure-measuring devices are calibrated to read zero in the atmosphere, and so they indicate gage pressure.Vacuum pressures: Pressures below atmospheric pressure. 5
Pressure at a Point Pressure is the compressive force per unit area but it is not a vector. Pressure at any point in a fluid is the same in all directions. Pressure has magnitude but not a specific direction, and thus it is a scalar quantity. Pressure is a scalar quantity, not a vector; the pressure at aForces acting on a wedge-shaped point in a fluid is the same in allfluid element in equilibrium. directions. 7
Variation of Pressure with Depth When the variation of density with elevation is knownThe pressure of a fluid at rest Free-body diagram of a rectangularincreases with depth (as a fluid element in equilibrium. 8result of added weight).
Pressure in a liquid at In the case of gas, the variation ofrest increases linearly pressure with height is negligible.with distance from thefree surface. 9
The pressure is the same at all points on a horizontal plane in agiven fluid regardless of geometry, provided that the points areinterconnected by the same fluid. 10
PRESSURE MEASUREMENT DEVICES The Barometer• Atmospheric pressure is measured by a device called a barometer; thus, the atmospheric pressure is often referred to as the barometric pressure.• A frequently used pressure unit is the standard atmosphere, which is defined as the pressure produced by a column of mercury 760 mm in height at 0°C (ρHg = 13.595 kg/m3) under standard gravitational acceleration (g = 9.807 m/s2). The length or the cross-sectional area of the tube has no effect on the height of the fluid column of a barometer, provided that the tube diameter is large enough to avoid surface tension (capillary) effects. The basic barometer. 12
The variation of gagepressure with depth inthe gradient zone of thesolar pond. 15
MEASUREMENT OF PRESSURE USING VARIOUS KINDS OF MANOMETERS
PASCAL’S LAW Pascal’s law: Any two points at the same elevation a continuous mass of the same static fluid will be at the same pressure. The idea of jumping across to equal pressures facilitates manometer calculations.11-15 January 2010 M Subramanian
MANOMETERIt is commonly used to measure small andmoderate pressure differences. A manometercontains one or more fluids such as mercury,water, alcohol, or oil. Measuring the pressure drop across a flow section or a flow device by a differential manometer The basic manometerIn stacked-up fluid layers, thepressure change across a fluidlayer of density ρ and height h is 18ρgh.
MANOMETER CALCULATIONS Simple U-tube manometer11-15 January 2010 M Subramanian
INVERTED U-TUBE MANOMETER11-15 January 2010 M Subramanian
OTHER TYPES OF MANOMETER11-15 January 2010 M Subramanian
MULTI-TUBE MANOMETER11-15 January 2010 M Subramanian
OTHER PRESSURE MEASUREMENT DEVICES• Bourdon tube: Consists of a hollow metal tube bent like a hook whose end is closed and connected to a dial indicator needle.• Pressure transducers: Use various techniques to convert the pressure effect to an electrical effect such as a change in voltage, resistance, or capacitance.• Pressure transducers are smaller and faster, and they can be more sensitive, reliable, and precise than their mechanical counterparts.• Strain-gage pressure transducers: Work by having a diaphragm deflect between two chambers open to the pressure inputs. Pressure transducers• Piezoelectric transducers: Also called solid-state pressure transducers, work on the principle that an electric potential is generated in a crystalline substance when it is subjected to mechanical pressure. 26 Piezoelectric pressure transducers
PASCAL’S LAWThe pressure applied to a confined fluid increases the pressurethroughout by the same amount.The area ratio A2/A1 iscalled the ideal mechanicaladvantage of the hydrauliclift. Lifting of a large weight by a small force by the application of Pascal’s law. 27
Deadweight tester: Another type of mechanical pressure gage. It is usedprimarily for calibration and can measure extremely high pressures.A deadweight tester measures pressure directly through application of aweight that provides a force per unit area—the fundamental definition ofpressure.It is constructed with an internal chamber filled with a fluid (usually oil),along with a tight-fitting piston, cylinder, and plunger.Weights are applied to the top of the piston, which exerts a force on the oilin the chamber. The total force F acting on the oil at the piston–oil interfaceis the sum of the weight of the piston plus the applied weights. A deadweight tester is able to measure extremely high pressures (up to 70 MPa in 28 some applications).
Any Questions?11-15 January 2010 M Subramanian