FLUID MECHANICS

where: At standard condition  W = 1000 kg/m 3  W = 9.81 KN/m 3

Atmospheric pressure: The pressure exerted by the atmosphere. At sea level condition: Pa = KPa = Mpa = Bar = 760 mm Hg = m H 2 O = kg/cm 2 = 14.7 psi = in Hg = ft H 2 O Absolute and Gage Pressure Absolute Pressure: is the pressure measured referred to absolute zero and using absolute zero as the base. Gage Pressure: is the pressure measured referred to atmospheric pressure, and using atmospheric pressure as the base

Atmospheric Pressure At mospheric pressure is normally about 100,000 Pa Differences in atmospheric pressure cause winds to blow – Low atmospheric pressure inside a hurricane’s eye contributes to the severe winds and the development of the storm surge

x dx v+dv v moving plate Fixed plate v S  dv/dx S =  (dv/dx) S =  (v/x)  = S/(v/x) where:  - absolute or dynamic viscosity in Pa-sec S - shearing stress in Pascal v - velocity in m/sec x -distance in meters

 r h   Where:  - surface tension, N/m  - specific weight of liquid, N/m 3 r – radius, m h – capillary rise, m CC  Surface Tension of Water

MANOMETERS Manometer is an instrument used in measuring gage pressure in length of some liquid column.  Open Type Manometer : It has an atmospheric surface and is capable in measuring gage pressure.  Differential Type Manometer : It has no atmospheric surface and is capable in measuring differences of pressure. Pressure Head: where: p - pressure in KPa  - specific weight of a fluid, KN/m 3 h - pressure head in meters of fluid

In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point changes as time passes. Turbulent flow is an extreme kind of unsteady flow in which the velocity of the fluid particles at a point change erratically in both magnitude and direction. Types of flowing fluids:

More types of fluid flow Fluid flow can be compressible or incompressible. Most liquids are nearly incompressible. Fluid flow can be viscous or nonviscous. An incompressible, nonviscous fluid is called an ideal fluid.

When the flow is steady, streamlines are often used to represent the trajectories of the fluid particles.

The Equation of Continuity

EQUATION OF CONTINUITY The mass flow rate has the same value at every position along a tube that has a single entry and a single exit for fluid flow. SI Unit of Mass Flow Rate: kg/s

Open Type Manometer Open Manometer Fluid Fluid A Differential Type Manometer Fluid B Manometer Fluid Fluid A

Determination of S using a U - Tube x y Open Fluid A Fluid B S A x = S B y

Energy and Head Bernoullis Energy equation: Reference Datum (Datum Line) 1 2 z1z1 Z2Z2 H L =  U - Q

BERNOULLI’S EQUATION In steady flow of a nonviscous, incompressible fluid, the pressure, the fluid speed, and the elevation at two points are related by:

1. Without Energy head added or given up by the fluid (No work done by the system or on the system: 2. With Energy head added to the Fluid: (Work done on the system) 3. With Energy head added given up by the Fluid: (Work done by the system) Where: P – pressure, KPa - specific weight, KN/m3 v – velocity in m/secg – gravitational acceleration Z – elevation, metersm/sec2 + if above datumH – head loss, meters - if below datum

Ventury Meter A. Without considering Head loss inlet throat exit Manometer 1 2 B. Considering Head loss Meter Coefficient

Orifice: An orifice is an any opening with a closed perimeter Without considering Head Loss 11 22 a a Vena Contracta h By applying Bernoulli's Energy theorem: But P 1 = P 2 = P a and v 1 is negligible, then and from figure: Z 1 - Z 2 = h, therefore Let v 2 = v t where: v t - theoretical velocity, m/sec h - head producing the flow, meters g - gravitational acceleration, m/sec 2

where: v' - actual velocity v t - theoretical velocity a - area of jet at vena contracta A - area of orifice Q' - actual flow Q - theoretical flow Cv - coefficient of velocity Cc - coefficient of contraction Cd - coefficient of discharge

Lower Reservoir Upper Reservoir Suction GaugeDischarge Gauge Gate Valve Gate Valve

2. DISCHARGE or CAPACITY Q = A s v s = A d v d m 3 /sec

HYDRO ELECTRIC POWER PLANT Headrace Tailrace Y – Gross Head Penstock turbine 1 2

Headrace Tailrace Y – Gross Head Penstock ZBZB 1 2 Draft Tube B Generator B – turbine inlet

Pump-Storage Hydroelectric power plant: During power generation the turbine-pump acts as a turbine and during off-peak period it acts as a pump, pumping water from the lower pool (tailrace) back to the upper pool (headrace). Turbine-Pump