FLUID MECHANICS PRINCIPLES OF HYDROSTATIC When the fluid is at rest relative at the surface, does the viscosity of the fluid will have a shearing effect on the surface? In general, fluids can exert both normal and shear forces on their surfaces of contact. However, if the fluid is at rest relative to the surface, then the viscosity of the fluid will have no shearing effect on the surface. Instead, the only force the fluid exerts is a normal force, and the effect of this force is called pressure. PRESSURE (p) Pressure is defined as a normal force exerted by a fluid per unit area. If force is distributed uniformly into the area, we can say: 𝐹 p= 𝐴 𝑢𝑛𝑖𝑡: ES: psi ; SI: 𝑘𝑔 IU: 2 𝑜𝑟 𝑐𝑚 𝑁 𝑚2 𝑜𝑟 𝑃𝑎𝑠𝑐𝑎𝑙 𝑖𝑛 𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒𝑠 𝑢𝑛𝑖𝑡 𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 𝑎𝑡𝑚 = 1.03323 = 14.696 𝑘𝑔 𝑐𝑚2 𝑙𝑏 𝑖𝑛2 PASCAL’S LAW Pascal’s Law was developed by French Mathematician, Blaise Pascal. This law states that the pressure on a fluid is equal to all direction and in all part of the container. Other pressure units commonly used in practice, especially in Europe, are bar and standard atmosphere. 1 bar = 105 Pa = 100 kPa 1 atm = 101,325 Pa = 101.325 kPa = 760 mm Hg (mercury barometer) GAUGE PRESSURE Gauge pressure are pressures above or below the atmosphere and can be measured by pressure gauges or manometers. GAUGE PRESSURE Gauge pressure are pressures above or below the atmosphere and can be measured by pressure gauges or manometers. ATMOSPHERIC PRESSURE Pressure at any point in the earth from the weight of the air above it. 𝑝𝑎𝑡𝑚 ABSOLUTE PRESSURE Pressure above absolute zero (vacuum). Vacuum is a space that has all matter removed from it. 𝑝𝑎𝑏𝑠 = 𝑝𝑔𝑎𝑢𝑔𝑒 + 𝑝𝑎𝑡𝑚 Note: Absolute zero is attained if all air is removed. Absolute pressure can never be negative. Determine the absolute pressure inside a closed tank with a vacuum pressure of 30 kPa. Assume standard atmospheric pressure. PRESSURE VARIATIONS PRESSURE VARIATIONS PRESSURE VARIATIONS PRESSURE VARIATIONS PRESSURE HEAD MEASUREMENT OF STATIC PRESSURE BAROMETER A barometer is a device for measuring atmospheric pressure. MEASUREMENT OF STATIC PRESSURE BAROMETER A barometer reads 760 mmHg and a pressure gauge attached to a tank reads 850 cm of oil (sp.gr 0.80). What is the absolute pressure in the tank in kPa? MEASUREMENT OF STATIC PRESSURE MANOMETERS A manometer is a simple and measuring pressure and pressure bent to form a U-tube and filled specific gravity. The surface of proportion to changes in pressure. inexpensive device for difference. It is usually with a liquid of known the liquid will move in MEASUREMENT OF STATIC PRESSURE PIEZOMETER Piezometer is the simplest form of manometer which is tapped into the wall of pressure conduit for the purpose of measuring pressure. Though effective in many purposes, the piezometer is not practical to use in lighter liquids with large pressure and cannot be used to measure gas pressure. MEASUREMENT OF STATIC PRESSURE PIEZOMETER Determine the height of the liquid will rise in the piezometers of shown in the figure if the pressure at M is 68.95 kPa and the liquid is (a) water, (b) oil (sp gr 0.85), (c) mercury? MEASUREMENT OF STATIC PRESSURE OPEN MANOMETER Open manometer is a tube bent into a U-shape to contain one or more fluids of different specific gravities. MEASUREMENT OF STATIC PRESSURE OPEN MANOMETER Determine the pressure at the center of the pipe. MEASUREMENT OF STATIC PRESSURE OPEN MANOMETER Determine the pressure at the center of the pipe. MEASUREMENT OF STATIC PRESSURE MANOMETERS MEASUREMENT OF STATIC PRESSURE DIFFERENTIAL MANOMETER Differential manometer cannot measure pressure but can measure pressure difference. Frequently in hydraulic problems, the difference in pressure is more useful information than the pressure itself. MEASUREMENT OF STATIC PRESSURE DIFFERENTIAL MANOMETER For the manometer setup shown, determine the difference in pressure between A and B. HYDRAULIC SYSTEM Solve the following problem with a little help from the diagram above of a simple hydraulic system of two pistons and cylinders connected together. The cross-section area of piston A1 is 0.000400 m2. The cross-section area of piston A2 is 0.00800 m2. HYDRAULIC SYSTEM (a) If a force of 40 N (F1) is applied to piston 1, calculate the pressure created in the fluid. (b) Calculate the force F2 created by the force of 40 N on piston A1. HYDRAULIC SYSTEM (d) In order to create a force of 2000 N from cylinder 2, what should the cross-section area of piston 2 be if the force applied to piston 1 is still 40 N?
