Chapter 2. Fluid Statics - engr.uconn.eduengr.uconn.edu/~rzr11001/ME3250_F12/ch2...
Transcript of Chapter 2. Fluid Statics - engr.uconn.eduengr.uconn.edu/~rzr11001/ME3250_F12/ch2...
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Chapter 2. Fluid Statics
� Topics
� Fluid at rest: No relative motion/deformation: no shearing stress
� Hydrostatic pressure at a point: Pascal’s Law
� Pressure field/pressure variation for fluids at rest
� Measurement of pressure
� Hydrostatic force on surfaces� Vertical/Horizontal planes
� Inclined surfaces
� Curved surfaces
� Buoyancy, flotation, and stability
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Pressure Field in Static Fluids
� Static fluids
� no shearing stress
� no fluid deformation
� “F = m*a” can be applied on a control volume as if on a rigid body
� We are interested in the balance between the hydrostatic force and body forces on a control volume
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Pressure at a point
� Pascal’s Law: px = py = pz at any point in static fluid
i.e. pressure is isotropic
WU1
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Slide 3
WU1 On whiteboard, show the derivationWindows User, 1/6/2012
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Hydrostatic Force on a
Small Control Volume
� dfs = ∇p*dv
� −�� − ��� = �
∫=A
Apdfvv
∫=A
xx pdAf
WU2
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Slide 4
WU2 How the pressure in a fluid in which there are no shearing stresses vary from point to point?
Show derivation, introduce the pressure derivativeWindows User, 1/6/2012
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Pressure Field for Incompressible Fluids
� −�� − ��� =0
� ∆p = ρgh
� How about compressible fluids?
r1r2
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Slide 5
r1 rzr11001, 1/8/2012
r2 show derivation
hydrostatic distribution; The pressure difference between two points can be specified by the distance h, which is called pressure headrzr11001, 1/8/2012
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Example: atmosphere
r3
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Slide 6
r3 show the derivation for isothermal case with ideal gas lawrzr11001, 1/8/2012
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Figure 2.9 (p. 51) Piezometer tube.
Pressure Measurement:
Piezometer-Tube Manometer
• Absolute Pressure:relative to vacuum
• Gage Pressure:relative to ambient
� = −�1ℎ1
r4r5
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Slide 7
r4 Manometers use vertical or inclined liquid columns to measure pressurerzr11001, 1/8/2012
r5 Disvantages:1. the pressure in the container must be greater than atmospheric pressure2. pressure difference relative smallrzr11001, 1/8/2012
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Figure 2.10 (p. 51)Simple U-tube manometer.
Pressure Measurement:
U-Tube Manometer
� = �2ℎ2 − �1ℎ1
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Figure 2.12 (p. 54)Inclined-tube manometer
Pressure Measurement:
Inclined-Tube Manometer
� − �� = �2�2���θ
r6
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Slide 9
r6 To measure small pressure differencerzr11001, 1/8/2012
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Hydrostatic Force on a Surface
� Differential form
� Integral form:
Apdfdvv
=
∫=A
Apdfvv
∫=A
xx pdAf
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Ex: Hydrostatic Force on Planes
� Horizontal planes � Vertical planes
r7
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Slide 11
r7 resultant force
Derive Equation 2.18
Explain pressure prism. Only good for rectangularrzr11001, 1/8/2012
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Ex:
Hydrostatic Force on Curved Surfaces
r8
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Slide 12
r8 Show derivation by considering the eqiulibrium of the fluid volume enclosed by the curved surface of interest and thr horizontal and vertial projections of this surface.rzr11001, 1/8/2012
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Buoyancy
� Buoyancy: integrated hydraulic force on the surface of an object
� Archimedes principle:
� Buoyancy force = weight of the displaced volume
r9
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Slide 13
r9 show the derivation procedure on Page 69rzr11001, 1/8/2012
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Stability
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Pressure Variation under Acceleration
Linear Acceleration
Rigid Body Rotation
−�� − ��� = �