CE 204 Fluid Mechanics 1 Onur Akay, Ph.D

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Onur AKAY Onur AKAY Onur AKAY Onur AKAY

Assistant Professor Assistant Professor Assistant Professor Assistant Professor Assistant Professor

Okan University Okan University Okan University Okan University Okan University

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

Akfırat Campus Akfırat Campus Akfırat Campus Akfırat Campus

34959 Tuzla-Istanbul/TURKEY 34959 Tuzla-Istanbul/TURKEY 34959 Tuzla-Istanbul/TURKEY 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Phone: +90-216-677-1630 ext.1974 Phone: +90-216-677-1630 ext.1974 Phone: +90-216-677-1630 ext.1974

Fax: +90-216-677-1486 Fax: +90-216-677-1486 Fax: +90-216-677-1486 Fax: +90-216-677-1486 E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]

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

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

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.

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.

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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 sphere

walls of sphere walls of sphere walls of sphere

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

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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 pressure in the balloon is 0.2 meter of water:

p=0.2 m-H O p=0.2 m-H O p=0.2 m-H₂O p=0.2 m-H₂₂O

Convert to other units using Table F.1.

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

0.2 meter 0.2 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 kPa

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

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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.

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.

*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 either

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

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

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 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.

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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.

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).

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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.

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

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

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

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

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Piezometric head, h, characterizes hydrostatic Piezometric head, h, characterizes hydrostatic Piezometric head, h, characterizes hydrostatic Piezometric head, h, characterizes hydrostatic equilibrium.

equilibrium.

h = h = h h = h = h h_d = h_e = h_f h_d = h_e = h_f h_d = h_e = h_f

h ≠ h h ≠ h h_c ≠ h_d h_c_c ≠ h_d_d

h = h = h h = h = h h_a = h_b = h_c h_a = h_b = h_c

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

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Pressure Measurements:

Barometer: Measure atmospheric pressure.

p = 2.4 x 10^-6 atm p_v = 2.4 x 10^-6 atm p_v = 2.4 x 10^-6 atm p_v = 2.4 x 10 atm

Apply the hydrostatic equation:

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

The gage pressure at the center of the pipe:

p = h p = h p = h p = h

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

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

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Forces on Plane Surfaces:

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.

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Forces on Plane Surfaces:

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

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Magnitude of Resultant Hydrostatic Force:

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Line of Action of the Resultant Force:

Area Area Area Area

Moment of Moment of Moment of Moment of Inertia

Inertia Inertia Inertia

- 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

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