m2ws1.pdf

Fluid Mechanics Dr. Jagadish Torlapati Fall 2019 MODULE 2 – FLUID STATICS WORKSHEET 1 – PRESSUDE DISTRIBUTION WITHIN A FLUID Learning outcomes 1. Describe pressure and its variation within a...

Fluid Mechanics Dr. Jagadish Torlapati Fall 2019 MODULE 2 – FLUID STATICS WORKSHEET 1 – PRESSUDE DISTRIBUTION WITHIN A FLUID Learning outcomes 1. Describe pressure and its variation within a stationary fluid 2. List the methods for computation of pressure at a specific depth 3. Compute resultant hydrostatic force and its location on a submerged surface 4. Describe the principles of buoyancy and stability 1.1 Pressure Pressure is defined as the normal force per unit area (P=F/A). The units are N/m2, psf (lb/ft2) and psi (lb/in2). Pascal’s law states that the pressure acting at a point in a fluid is same in all directions. The pressure in vacuum is zero and this is defined as zero-absolute pressure. The pressures measured in reference to this pressure are called absolute pressures (pabs). The pressure measured at sea level at a temperature of 15 C is called standard atmospheric pressure (patm). The pressures measured in reference to this pressure are called gage pressures (pg). All the pressures used in this course will be gage pressures unless otherwise stated. Pressure in a continuously distributed uniform static liquid varies only with vertical distance and is independent of the shape of the container. The pressure is the same at all points on a given horizontal plane in the fluid. The pressure increases with depth in a fluid. This is intuitive because the weight of the fluid increases as you go downwards increasing the pressure. 𝑝 Pressure head (h) is the height of the liquid required to produce 1 atmospheric pressure. ℎ = 𝛾 Compute the pressure head for mercury (Hg) and water column? 1  Fluid Mechanics Dr. Jagadish Torlapati Fall 2019 Problem 1 The tank and drainpipe are filled with gasoline and glycerin to the depths shown in the figure. Determine the pressure on the drain plug at C. Report the answer as a pressure head in feet of water. Take γg= 45.3 lb/ft3 and γgl=78.7 lb/ft3 1.2 Pressure variation within compressible fluids When the fluid is compressible, its specific weight is a varies with pressure and temperature We need to use the ideal gas law to establish a relationship between pressure, temperature and specific weight. Problem 2 The natural gas in a storage tank is contained within a flexible membrane and held under constant pressure using a weighted top that can move up and down as the gas enters or leaves the tank. Determine the required weight of the top if the gage pressure at the outlet A is to be 60 kPa. The gas a constant temperature of 20 C. (compare the results assuming the gas to be both incompressible and compressible) 2  Fluid Mechanics Dr. Jagadish Torlapati Fall 2019 1.3 Measurement of pressure Atmospheric pressure is measured using a barometer. A manometer is used to measure the gage pressure in a liquid. Negative or moderately high gage pressures are measured using a U-tube manometer. Differential manometer is used to measure the pressure difference at two points. There are also other measuring devices such as Bourdon gage, pressure transducers and other pressure gages. Would you use a low or high specific gravity liquid to measure low pressures? Manometer rule – Start at a point where the pressure is to be determine and proceed to add to it the pressures algebraically from one vertical fluid interface to the next until you reach the liquid surface at the other end of the manometer Problem 3 A funnel is fitted with oil and water to the levels shown while portion CD of the tube contains mercury. Determine distance h the mercury level is from the top of the oil surface. Use ρoil as 880 kg/m3, ρwater = 1000 kg/m3 and ρmercury as 13550 kg/m3 3  Fluid Mechanics Dr. Jagadish Torlapati Fall 2019 Problem 4 Determine the difference in pressure between the centerline points A and B in the two pipelines, if the manometer liquid CD is at the level shown. The density of the liquid in AC and DB is rho = 800 kg/m3 and in CD rho cd = 1100 kg/m3 4