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III. Fluid Statics Slide 2 Contents 1. Pressure in Static Fluid 2. Governing Equation 3. Units and Scales of Pressure 4. Pressure Measurement 5. Fluid Force on Plane Surface 6. Fluid Force on Curved Surface 7. Relative Equilibrium Slide 3 1. Pressure in Static Fluid Slide 4 There is only inward-normal stress (pressure) on any contact area at a point in static fluid Slide 5 The magnitude of the pressure at any point in static fluid is independent of the direction Slide 6 Slide 7 Forces Slide 8 Forces Balance Slide 9 Force Balance Slide 10 1. 1.There is only inward-normal stress (pressure) on any contact area at a point in static fluid (by definition) 2. 2.The magnitude of the pressure at any point in static fluid is independent of the direction (by force balance) Stress state in static fluid can be described by a SCALAR Slide 11 State of Stress In generalIn static fluids Slide 12 2. Basic Equation Slide 13 Forces on a fluid element Slide 14 Force balance Slide 15 Force Balance Slide 16 Governing Equation Slide 17 The gradient of pressure is balanced by the body force Slide 18 In the case of conservative force Y = Force potential Slide 19 When gravity force is the only external force ( z axis is vertically upward ) Slide 20 Let h = -z ( h is the depth below a datum ) Pressure in a static fluid is linearly proportional to the depth below a datum Slide 21 Slide 22 Slide 23 z = constant Horizontal plane in static fluid is necessarily equi-pressure plane p = constant Slide 24 Slide 25 ? ? Slide 26 Piezometric head in a static fluid is constant Position Head Pressure Head Piezometric head Slide 27 1 2 Slide 28 3. Units and Scales of Pressure Slide 29 Reference of pressure is taken at ZERO Absolute Pressure P A Relative Pressure P R Reference of pressure is taken at p 0 P R = Gage pressure P atm - P A = Vacuum pressure Slide 30 Slide 31 Pressure measured by fluid force per unit area Pressure measured by equivalent height of liquid 1 atm = 1.034 at = 101325 Pa = 760 mm Hg = 10.34 m H 2 O Pressure measured by atmospheric pressure Slide 32 4. Pressure Measurement Slide 33 Barometer Slide 34 Piezometer h Slide 35 Manometer h1h1h1h1 h2h2h2h2 Slide 36 Manometer for negative pressure h1h1h1h1 h2h2h2h2 Slide 37 Differential Manometer hBhBhBhB hAhAhAhA DhDhDhDh DzDzDzDz Slide 38 5. Fluid Force on Plane Surface Slide 39 Slide 40 x y Slide 41 Centroid Slide 42 Centroid Slide 43 Centre of pressure Slide 44 PropertiesofAreas Slide 45 Example Rock-fill Porous Water Impermeable Curtain Impermeable Layer Concrete Cover 2 1 h l Slide 46 Example On the slope On the bottom Slide 47 6. Fluid Force on Curved Surface Slide 48 Slide 49 S AzAz AxAx AyAy p Slide 50 Fluid Force Slide 51 Slide 52 Slide 53 Example 30 d Slide 54 Horizontal Force No net force h Slide 55 Vertical Force Slide 56 Force Balance Slide 57 Buoyancy Slide 58 Stability of Floating Bodies Slide 59 7. Relative Equilibrium Slide 60 Static state of fluid in a moving coordinate system is called relative equilibrium Slide 61 Basic Equation DAlemberts Principle Slide 62 Uniform Acceleration Equi-pressure surface Slide 63 Uniform Rotation Equi-pressure surface