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Chapter 3 Fluid StaticsChapter 3 Fluid StaticsChapter 3 Fluid Statics

Pressure variation w/ elevation, Pressure Measurements, Forces on Plane SurfacesPressure variation w/ elevation, Pressure Measurements, Forces on Plane SurfacesPressure variation w/ elevation, Pressure Measurements, Forces on Plane Surfaces

Onur AKAYOnur AKAYOnur AKAYOnur AKAY

Assistant ProfessorAssistant ProfessorAssistant ProfessorAssistant ProfessorAssistant Professor

Okan UniversityOkan UniversityOkan UniversityOkan UniversityOkan University

Department of Civil EngineeringDepartment of Civil EngineeringDepartment of Civil EngineeringDepartment of Civil Engineering

Akfırat CampusAkfırat CampusAkfırat CampusAkfırat Campus

34959 Tuzla-Istanbul/TURKEY34959 Tuzla-Istanbul/TURKEY34959 Tuzla-Istanbul/TURKEY34959 Tuzla-Istanbul/TURKEY

Phone: +90-216-677-1630 ext.1974Phone: +90-216-677-1630 ext.1974Phone: +90-216-677-1630 ext.1974Phone: +90-216-677-1630 ext.1974

Fax: +90-216-677-1486Fax: +90-216-677-1486Fax: +90-216-677-1486Fax: +90-216-677-1486

E-mail: [email protected]: [email protected]: [email protected]: [email protected]

Onur Akay, Ph.D. CE 204 Fluid Mechanics 1Onur Akay, Ph.D. CE 204 Fluid Mechanics 1Onur Akay, Ph.D. CE 204 Fluid Mechanics 1



Fluid statics is restricted to fluids that are in hydrostatic equilibrium.Fluid statics is restricted to fluids that are in hydrostatic equilibrium.Fluid statics is restricted to fluids that are in hydrostatic equilibrium.Fluid statics is restricted to fluids that are in hydrostatic equilibrium.

Equilibrium of a fluid particle:Equilibrium of a fluid particle:Equilibrium of a fluid particle:Equilibrium of a fluid particle:

A fluid particle is defined as a body of fluid having finite mass and internal structure but A fluid particle is defined as a body of fluid having finite mass and internal structure but A fluid particle is defined as a body of fluid having finite mass and internal structure but A fluid particle is defined as a body of fluid having finite mass and internal structure but

negligible dimensions.negligible dimensions.negligible dimensions.negligible dimensions.negligible dimensions.

Hydrostatic condition: Each fluid particle is in force equilibrium with the net force due to Hydrostatic condition: Each fluid particle is in force equilibrium with the net force due to Hydrostatic condition: Each fluid particle is in force equilibrium with the net force due to Hydrostatic condition: Each fluid particle is in force equilibrium with the net force due to

pressure balancing the weight of the fluid particle.pressure balancing the weight of the fluid particle.pressure balancing the weight of the fluid particle.pressure balancing the weight of the fluid particle.




Pressure: The ratio of normal force to area at a point.Pressure: The ratio of normal force to area at a point.Pressure: The ratio of normal force to area at a point.Pressure: The ratio of normal force to area at a point.

Pressure acting on the Pressure acting on the Pressure acting on the Pressure acting on the

walls of spherewalls of spherewalls of spherewalls of sphere

Pressure is a scalar quantity; that is, it has magnitude only.Pressure is a scalar quantity; that is, it has magnitude only.Pressure is a scalar quantity; that is, it has magnitude only.Pressure is a scalar quantity; that is, it has magnitude only.

Units: - Force to area(Newtons per square meter of area-Pa)Units: - Force to area(Newtons per square meter of area-Pa)Units: - Force to area(Newtons per square meter of area-Pa)Units: - Force to area(Newtons per square meter of area-Pa)

- The height of a column of liquid. - The height of a column of liquid. - The height of a column of liquid. - The height of a column of liquid.




Pressure is a scalar quantity; that is, it has magnitude only.Pressure is a scalar quantity; that is, it has magnitude only.Pressure is a scalar quantity; that is, it has magnitude only.Pressure is a scalar quantity; that is, it has magnitude only.

Units: - Force to area(Newtons per square meter of area-Pa)Units: - Force to area(Newtons per square meter of area-Pa)Units: - Force to area(Newtons per square meter of area-Pa)Units: - Force to area(Newtons per square meter of area-Pa)

- The height of a column of liquid. - The height of a column of liquid. - The height of a column of liquid. - The height of a column of liquid.

*The pressure in the balloon is 0.2 meter of water:*The pressure in the balloon is 0.2 meter of water:*The pressure in the balloon is 0.2 meter of water:*The pressure in the balloon is 0.2 meter of water:

p=0.2 m-H Op=0.2 m-H Op=0.2 m-H2Op=0.2 m-H2O2

Convert to other units using Table F.1.Convert to other units using Table F.1.0.2 meter

Convert to other units using Table F.1.0.2 meter

Convert to other units using Table F.1.0.2 meter0.2 meter

p= (p=0.2 m-H O) x (101.3 kPa/10.33 m-H O)p= (p=0.2 m-H O) x (101.3 kPa/10.33 m-H O)p= (p=0.2 m-H2O) x (101.3 kPa/10.33 m-H2O)p= (p=0.2 m-H2O) x (101.3 kPa/10.33 m-H2O)p= (p=0.2 m-H2O) x (101.3 kPa/10.33 m-H2O)

p= 1.96 kPap= 1.96 kPap= 1.96 kPap= 1.96 kPa




Absolute Pressure: The pressure in a perfect vacuum is called absolute zero, and pressure Absolute Pressure: The pressure in a perfect vacuum is called absolute zero, and pressure Absolute Pressure: The pressure in a perfect vacuum is called absolute zero, and pressure Absolute Pressure: The pressure in a perfect vacuum is called absolute zero, and pressure

measured relative to this zero pressure is termed absolute pressure.measured relative to this zero pressure is termed absolute pressure.measured relative to this zero pressure is termed absolute pressure.measured relative to this zero pressure is termed absolute pressure.

Gage Pressure: When pressure is measured relative to prevailing local atmospheric Gage Pressure: When pressure is measured relative to prevailing local atmospheric Gage Pressure: When pressure is measured relative to prevailing local atmospheric Gage Pressure: When pressure is measured relative to prevailing local atmospheric

pressure, the pressure value is called gage pressure.pressure, the pressure value is called gage pressure.pressure, the pressure value is called gage pressure.pressure, the pressure value is called gage pressure.pressure, the pressure value is called gage pressure.

*For example, a gage pressure of 50 kPa recorded in a location where the atmospheric *For example, a gage pressure of 50 kPa recorded in a location where the atmospheric *For example, a gage pressure of 50 kPa recorded in a location where the atmospheric *For example, a gage pressure of 50 kPa recorded in a location where the atmospheric

pressure is 100 kPa is expressed as eitherpressure is 100 kPa is expressed as eitherpressure is 100 kPa is expressed as eitherpressure is 100 kPa is expressed as either

p= 50 KPa gage or p= 150 kPa absp= 50 KPa gage or p= 150 kPa absp= 50 KPa gage or p= 150 kPa absp= 50 KPa gage or p= 150 kPa abs

Vacuum pressure: The difference between atmospheric pressure and actual pressure.Vacuum pressure: The difference between atmospheric pressure and actual pressure.Vacuum pressure: The difference between atmospheric pressure and actual pressure.Vacuum pressure: The difference between atmospheric pressure and actual pressure.Vacuum pressure: The difference between atmospheric pressure and actual pressure.

*For example, if a gage connected to a tank indicates a vacuum pressure of 31.0 kPa, this *For example, if a gage connected to a tank indicates a vacuum pressure of 31.0 kPa, this *For example, if a gage connected to a tank indicates a vacuum pressure of 31.0 kPa, this *For example, if a gage connected to a tank indicates a vacuum pressure of 31.0 kPa, this

can also be stated as 70.0 kPa absolute, or -31.0 kPa gage.can also be stated as 70.0 kPa absolute, or -31.0 kPa gage.can also be stated as 70.0 kPa absolute, or -31.0 kPa gage.can also be stated as 70.0 kPa absolute, or -31.0 kPa gage.




Pascal’s Law: Pressure applied to an enclosed and continuous body of fluid is transmitted Pascal’s Law: Pressure applied to an enclosed and continuous body of fluid is transmitted Pascal’s Law: Pressure applied to an enclosed and continuous body of fluid is transmitted Pascal’s Law: Pressure applied to an enclosed and continuous body of fluid is transmitted

undiminished to every portion of that fluid and to the walls of the containing vessel.undiminished to every portion of that fluid and to the walls of the containing vessel.undiminished to every portion of that fluid and to the walls of the containing vessel.undiminished to every portion of that fluid and to the walls of the containing vessel.

Hydraulic machines use components such as pistons, pumps, and hoses to transmit forces Hydraulic machines use components such as pistons, pumps, and hoses to transmit forces Hydraulic machines use components such as pistons, pumps, and hoses to transmit forces Hydraulic machines use components such as pistons, pumps, and hoses to transmit forces

and energy using fluids (braking systems, forklift trucks, power steering systems, etc).and energy using fluids (braking systems, forklift trucks, power steering systems, etc).and energy using fluids (braking systems, forklift trucks, power steering systems, etc).and energy using fluids (braking systems, forklift trucks, power steering systems, etc).and energy using fluids (braking systems, forklift trucks, power steering systems, etc).




Pressure Variation with Elevation:Pressure Variation with Elevation:Pressure Variation with Elevation:Pressure Variation with Elevation:

The hydrostatic differential equation is derived by applying force equilibrium to a static The hydrostatic differential equation is derived by applying force equilibrium to a static The hydrostatic differential equation is derived by applying force equilibrium to a static The hydrostatic differential equation is derived by applying force equilibrium to a static

body of fluid.body of fluid.body of fluid.body of fluid.

Free-body DiagramFree-body DiagramFree-body DiagramFree-body Diagram




Simplify and divide by the volume of the body ∆l∆A to give Simplify and divide by the volume of the body ∆l∆A to give Simplify and divide by the volume of the body ∆l∆A to give Simplify and divide by the volume of the body ∆l∆A to give

Letting ∆z approach zero givesLetting ∆z approach zero givesLetting ∆z approach zero givesLetting ∆z approach zero gives

Hydrostatic Differential Equation:Hydrostatic Differential Equation:Hydrostatic Differential Equation:Hydrostatic Differential Equation:

+z direction/upward: pressure decreases+z direction/upward: pressure decreases+z direction/upward: pressure decreases+z direction/upward: pressure decreases

-z direction/downward: pressure increases-z direction/downward: pressure increases-z direction/downward: pressure increases-z direction/downward: pressure increases

along a horizontal plane: pressure remains constant along a horizontal plane: pressure remains constant along a horizontal plane: pressure remains constant along a horizontal plane: pressure remains constant along a horizontal plane: pressure remains constant




Hydrostatic Equation: Integrating assuming that specific weight γ is constant:Hydrostatic Equation: Integrating assuming that specific weight γ is constant:Hydrostatic Equation: Integrating assuming that specific weight γ is constant:Hydrostatic Equation: Integrating assuming that specific weight γ is constant:




Piezometric head, h, characterizes hydrostatic Piezometric head, h, characterizes hydrostatic Piezometric head, h, characterizes hydrostatic Piezometric head, h, characterizes hydrostatic

equilibrium.equilibrium.equilibrium.equilibrium.

h = h = hh = h = hhd = he = hfhd = he = hfhd = he = hf

h ≠ hh ≠ hhc ≠ hdhc ≠ hdc d

h = h = hh = h = hha = hb = hcha = hb = hc

Oil floating on waterOil floating on waterOil floating on waterOil floating on water




Pressure Measurements:Pressure Measurements:Pressure Measurements:Pressure Measurements:

Barometer: Measure atmospheric pressure.Barometer: Measure atmospheric pressure.Barometer: Measure atmospheric pressure.Barometer: Measure atmospheric pressure.

p = 2.4 x 10-6 atmpv = 2.4 x 10-6 atmpv = 2.4 x 10-6 atmpv = 2.4 x 10 atm

Apply the hydrostatic equation:Apply the hydrostatic equation:Apply the hydrostatic equation:Apply the hydrostatic equation:





Piezometer: Vertical tube in which a liquid rises in response to a positive gage pressure.Piezometer: Vertical tube in which a liquid rises in response to a positive gage pressure.Piezometer: Vertical tube in which a liquid rises in response to a positive gage pressure.Piezometer: Vertical tube in which a liquid rises in response to a positive gage pressure.

The gage pressure at the center of the pipe:The gage pressure at the center of the pipe:The gage pressure at the center of the pipe:The gage pressure at the center of the pipe:

p = hp = hp = hp = h





Manometer: Measure pressure by raising or lowering a column of liquid.Manometer: Measure pressure by raising or lowering a column of liquid.Manometer: Measure pressure by raising or lowering a column of liquid.Manometer: Measure pressure by raising or lowering a column of liquid.




Apparatus for determining change in piezometric head corresponding to flow in a pipe:Apparatus for determining change in piezometric head corresponding to flow in a pipe:Apparatus for determining change in piezometric head corresponding to flow in a pipe:Apparatus for determining change in piezometric head corresponding to flow in a pipe:




Forces on Plane Surfaces:Forces on Plane Surfaces:Forces on Plane Surfaces:Forces on Plane Surfaces:

A plane surface or panel is a flat surface of arbitrary shape.A plane surface or panel is a flat surface of arbitrary shape.A plane surface or panel is a flat surface of arbitrary shape.A plane surface or panel is a flat surface of arbitrary shape.

A description of the pressure at all points along a surface is called pressure distribution.A description of the pressure at all points along a surface is called pressure distribution.A description of the pressure at all points along a surface is called pressure distribution.A description of the pressure at all points along a surface is called pressure distribution.A description of the pressure at all points along a surface is called pressure distribution.

For a uniform pressure distribution, the CP is located at the centroid of area of the panel.For a uniform pressure distribution, the CP is located at the centroid of area of the panel.For a uniform pressure distribution, the CP is located at the centroid of area of the panel.For a uniform pressure distribution, the CP is located at the centroid of area of the panel.




Forces on Plane Surfaces:Forces on Plane Surfaces:Forces on Plane Surfaces:Forces on Plane Surfaces:

For a hydrostatic pressure distribution, the CP is located below the centroid of area.For a hydrostatic pressure distribution, the CP is located below the centroid of area.For a hydrostatic pressure distribution, the CP is located below the centroid of area.For a hydrostatic pressure distribution, the CP is located below the centroid of area.




Magnitude of Resultant Hydrostatic Force:Magnitude of Resultant Hydrostatic Force:Magnitude of Resultant Hydrostatic Force:Magnitude of Resultant Hydrostatic Force:

Hydrostatic force = (Pressure at the centroid of area) x (Panel area) Hydrostatic force = (Pressure at the centroid of area) x (Panel area) Hydrostatic force = (Pressure at the centroid of area) x (Panel area) Hydrostatic force = (Pressure at the centroid of area) x (Panel area)




Line of Action of the Resultant Force:Line of Action of the Resultant Force:Line of Action of the Resultant Force:Line of Action of the Resultant Force:

Area Area Area Area

Moment of Moment of Moment of Moment of

InertiaInertiaInertiaInertia

- Applies only to a single fluid of constant density- Applies only to a single fluid of constant density- Applies only to a single fluid of constant density- Applies only to a single fluid of constant density

- Pressure at liquid surface p=0 gage- Pressure at liquid surface p=0 gage- Pressure at liquid surface p=0 gage- Pressure at liquid surface p=0 gage

- Gives only the vertical location of the CP- Gives only the vertical location of the CP- Gives only the vertical location of the CP- Gives only the vertical location of the CP


onur akay assistant professor - okan Üniversitesi · onur akay assistant professor okan university...

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