Pressure Pressure is defined as the force exerted by a fluid per unit area. Units in SI are Pa=N/m2. The pressure unit Pascal is too small for pressure encountered in practice. Therefore, kPa and MPa are commonly used. Units in British are : psf = lbf/ft2, psi = lbf/in2 You have to convert from psi to psf ( 144 in2 = 1 ft2)

Pressure (continued) Absolute pressure, is measured relative to absolute vacuum (i.e., absolute zero pressure.) Gauge pressure, is measured relative to atmospheric pressure

Pressure (continued) Pgage is positive if the point above the Patm Pgage is negative if the point below the Patm called Vacuum

Pressure (continued) Variation of Pressure with Depth Pressure in fluid at rest does not change in the horizontal direction Remember the diver in a sea Pressure increases with depth in the vertical direction

pressure at a point The pressure at a point in a fluid has the same magnitude in all direction.

Pressure (continued) Variation of Pressure with Depth The pressure variation in a constant density static fluid is given as Pgage = Z Z is the vertical coordinate ( positive upward). is the specific weight of fluids, (N/m3) For small to moderate distances, the variation of pressure with height is negligible for gases because of their low density. Pabs = Pgage+Patm = Patm + rgh where h is the vertical elevation

The Manometer Specific gravity A device based on P /  = DZ is called a manometer and it is commonly used to measure small and moderate pressure differences. Specific gravity

Barometer and the Atmospheric Pressure The atmospheric pressure is measured by a device called a barometer; thus the atmospheric pressure is often referred to as the barometric pressure.

Barometer and the Atmospheric Pressure (continued) The standard atmospheric pressure is 760 mm Hg (29.92 in Hg) at 0oC. The unit of mm Hg is also called the torr in honor of Evangelista Torricelli (1608−1647). The length or the cross-sectional area of the tube has no effect on the height of the fluid column of a barometer.

Barometer and the Atmospheric Pressure (continued) Example 1-9: Effect of Piston Weight on Pressure in a Cylinder The piston of a vertical piston-cylinder device containing a gas has a mass of 60 kg and a cross-sectional area of 0.04 m2. The local atmospheric pressure is 0.97 bar, and the gravitational acceleration is 9.81 m/s2. (a) Determine the pressure inside the cylinder, (b) if some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change?

Barometer and the Atmospheric Pressure (continued)

Barometer and the Atmospheric Pressure (continued)

Example 1-7

Example 1-7

Differential pressure manometer Start from one point and go to the other point in the static fluid (+ down – up)

Pressure (continued) Pressure Variation in horizontal planes Pressure is constant in horizontal planes provided the fluid does not change. ( this leads to Pascal’s principle.) Noting that P1 = P2, the area ratio A2/A1 is called the ideal mechanical advantage. Using a hydraulic car jack with A2/A1 = 10, a person can lift a 1000-kg car by applying a force just 100 kgf (= 908 N).

Pressure Measurements Device U-tube anometer Bardoun tube Pressure transducer Diaphragm type Strain-gage Piezoelectric

Pressure Measurements Device

Problem Solving Technique The assumptions made while solving an engineering problem must be reasonable and justifiable. Step-by-step approach: Problem Statement Schematic Assumptions Physical Laws Properties Calculations Reasoning, Verification, and Discussion

Problem Solving Technique (continued) When solving problems, we will assume the given information to be accurate to at least 3 significant digits. Therefore, if the length of a pipe is given to be 40 m, we will assume it to be 40.0 m in order to justify using 3 significant digits in the final results. A result with more significant digits than that of given data falsely implies more accuracy.

Examples A pressure gage connected to a tank reads 500 kPa. The absolute pressure in the tank is to be determined . Pabs Patm = 94 kPa 500 kPa

Examples The pressure gage connected to a tank reads 15 kPa at a location where the barometer reading is 750 mmHg. Determine the absolute pressure of the tank. The density of mercury is given to be  = 13,590 kg/m3. Pabs Patm = 750 mmHg 15 kPa

Examples AIR Patm = 98 kPa 0.60 m The air pressure in a tank is measured by an oil manometer. For a given oil-level difference between the two columns, the absolute pressure in the tank is to be determined. The density of oil is given to be  = 850 kg/m3. AIR Patm = 98 kPa h=0.60 m

Examples 730 mmHg 755 mmHg h

Solution: Taking an air column between the top and the bottom of the mountain and writing a force balance per unit base area, we obtain OR follow the rule

Solution-continue