Chapter 3 Pressure and Fluid Statics Solutions Manual for Fluid Mechanics: Fundamentals and Applications CHAPTER 3 PRESSURE AND FLUID STATICS (original) (raw)
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Chapter 3 Pressure and Fluid Statics Chapter 3 PRESSURE AND FLUID STATICS
Pressure, Manometer, and Barometer 3-1C The pressure relative to the atmospheric pressure is called the gage pressure, and the pressure relative to an absolute vacuum is called absolute pressure. 3-2C The atmospheric air pressure which is the external pressure exerted on the skin decreases with increasing elevation. Therefore, the pressure is lower at higher elevations. As a result, the difference between the blood pressure in the veins and the air pressure outside increases. This pressure imbalance may cause some thin-walled veins such as the ones in the nose to burst, causing bleeding. The shortness of breath is caused by the lower air density at higher elevations, and thus lower amount of oxygen per unit volume. 3-3C No, the absolute pressure in a liquid of constant density does not double when the depth is doubled. It is the gage pressure that doubles when the depth is doubled. 3-4C If the lengths of the sides of the tiny cube suspended in water by a string are very small, the magnitudes of the pressures on all sides of the cube will be the same. 3-5C Pascal's principle states that the pressure applied to a confined fluid increases the pressure throughout by the same amount. This is a consequence of the pressure in a fluid remaining constant in the horizontal direction. An example of Pascal's principle is the operation of the hydraulic car jack. 3-6C The density of air at sea level is higher than the density of air on top of a high mountain. Therefore, the volume flow rates of the two fans running at identical speeds will be the same, but the mass flow rate of the fan at sea level will be higher. 3-7 The pressure in a vacuum chamber is measured by a vacuum gage. The absolute pressure in the chamber is to be determined. Analysis The absolute pressure in the chamber is determined from 24 kPa P abs kPa 68 = − = − = 24 92 vac atm abs P P P P atm = 92 kPa PROPRIETARY MATERIAL.
1. A cylinder contains a fluid at a gauge pressure of 360 KN/m 2. Express this pressure in terms of a head of (a) water, and (b) mercury of sp gr = 13.6 What would be the absolute pressure in the cylinder if atmospheric pressure is 760mm Hg. Solution: Pressure (P) = 360 KN/m 2 = 360x10 3 N/m 2 Head (h) = ? where ρ = Density of fluid a) Head in terms of water (ρ = 1000 kg/m 3) = 36.7m b) Head in terms of mercury ρ = sp gr x density of water = 13.6x1000 = 13600 kg/m 3 = 2.7m Atmospheric pressure (h) = 760mmhg = 0.76m hg Atmospheric pressure () = 101396N/m 2 = 101.3KN/m 2 Absolute pressure (Pabs) = ? Pabs = Pgauge + Patm = 360+101.3 = 461.3KN/m 2 2. What would the pressure in kN/m 2 be if the equivalent head is measured as 400mm of (a) mercury (sp gr 13.6) (b) water (c) oil specific weight 7.9 kN/m 3 (d) a liquid of density 520 kg/m 3 ? Solution: Head (h) = 400mm = 0.4m Pressure (P) =? where ρ = Density of fluid a) In terms of mercury, ρ = sp gr x density of water = 13.6x1000 = 13600 kg/m 3 = 13600x9.81x0.4 = 53366 N/m 2 = 53.366 KN/m 2 b) In terms of water, ρ = 1000 kg/m 3 = 1000x9.81x0.4 = 3924 N/m 2 = 3.924 KN/m 2 c) In terms of oil of sp. wt. () = 7.9 kN/m 3
What will be the (a) the gauge pressure and (b) the absolute pressure of water at depth 12m below the surface? water = 1000 kg/m 3 , and p atmosphere = 101kN/m 2. [117.72 kN/m 2 , 218.72 kN/m 2 ]
Chapter 13 Fluids Conceptual Problems
(c) Breathing in lowers one's average density and breathing out increases one's average density. Because denser objects float lower on the surface than do less dense objects, a floating person will oscillate up and down on the water surface as he or she breathes in and out.