BASINÇLI AKIM HİDROLİĞİ

HYDRAULICS OF PRESSURIZED FLOW_B.W.KARNEY
SAYFA 44
The term pressurized pipeline means a pipe system in which a free water surface is almost never found within the conduit. Mre precise is difficult because even in a pressurized pipe system, free surfaces are present within reserviors and tanks an sometimes can occur within the pipeline itself. However, in a pressurized system, the pressure within the conveyance system are usually well above atmospheric.

Modeling Approach
To model the behavior of the system, seek to answer where, what, how, where is resolved by assuming a direction of flow in each link. This gives an orientation to the specification of distance, discharge and velocity. Positive values indicate flow in the assumed direction

What is the material that makes up the pipe walls or fills the pipe. Water properties : density 1000kg/m3, density max at 4 C above freezing. high viscosity : .001 Ns/m2 )

How is based on three essential relations : 1.kinematic relation obtained from the law of mass conservation in a control volume. 2.equations of motion provided by both Newton's second law and the energy equation and 3.on equation of state adapted from compressibiliy considerations.

Conservation of Mass : key expression is the continuity or mass conservation equation. If for an isolated system, a quantity can be defined that remains precisely constant, the quantity is said to be absolutely conserved. (momentum, change, angular momentum)

1.Conservation of chemical species : molecular species are conserved in the absence of chemical reactions and atomic species are conserved in the absence of nuclear reactions.
DS=Sf-Si : balance final - balance initial, S'=ds/dt=I-O (S is the water stored in the control volume)

2.Steady Flow : I=O, inflow viAi = outflow viAi, assuming the flow is steady.
Q1+Q2 = Q3+Q4 (continuity at a pipe junction)

Newton's Second Law : It relates the changes in motion of a fluid or solid to the forces that cause the change. Thus, the result of all external forces acting on a system is equal to the rate of change of momentum of the system with respect to time.
Fext= d(mv)/dt = m dv/dt = ma

System Capacity : Problems in Time and Space
A transmission system is usually composed of a single-series line, as opposed to a distribution system that often consists of a complex network of interconnected pipes.

Issues of hydraulic capacity are usually answered by projecting demands and analyzing the system under steady flow conditions.

Questions about operation and sizing of pumping and reservoirs are answered by considering the gradual variation of demand over relatively short periods. In such cases, analysts use a quasi-steady approach. (F and E balances on the basis of steady, but the unsteady form is for the continuity so that flows can be accumulated and stored.)

Finally, the issue of required strenght, such as the pressure rating, is answered by considering transient conditions.

Steady flow, at a point flow do not change with the time. Otherwise, a flow is unsteady or transient. A more strictive definition is usually applied, temporal mean velocity does not change over periods.

Incompressible flow : if q is constant, it is said to be incompressible.

Steady Flow
Bernoulli equation : P/& + v2/2g + z (pressure head + velocity head + elevation head), H1=H2+hl, hl=L x S

Plot of pieozometric head called the HGL. A plot of total head is EGL.

The flow regime is classified by Re=vDl/m, Re<2000 - laminar flow, Re>4000 - turbulent, between transitional.

If the flow is turbulent, many small and abrupt variations in velocity in all directions occur. Moreover, the unsteady valves of instantaneous velocity will exist. Despite this, the mean values of velocity and pressure will be fixed as long as the external conditions do not change. It is in this sense that turbulent flows can be considered to be steady. Rapid mixing of turbulent flow can include detrimental reates of energy loss, high rates of corrosion, rapid scouring and erosion, excessive noise and vibration.

DW : hl=f L/D v2/2g (circular), D-4R (non-circular)
laminar f=Re/64
turbulent hl=f(Re, rel rough) - Moody/Colebrook-White

HW : Q=.278 C D2.63 S0.54 (S=hl/L), besides Swanee-Jain

DW equation is superior because it is theoretically based.

Local losses occurs for reasons other than wall friction, hl=K v2/2g

Pump supply Hp, key term is total dynamic head TDH. TDH varies with the discharge Q this H-Q is called the pump characteristics curve.
Hp=hp + v2/2g

Quasi Steady Flow System Operation
A common application arises in reservior engineering, in this case, the key step is to relate the rate of outflow, to the amount of water in the reservoir.

Unsteady Flow : Introduction of Fluid Transient
Pressure pipe systems are subjected to mechanical forces caused by fluid pressure, differential settlement and concentrated loads. In addition it must resist corrosion and chemical attacks. The internal pressure is of special importance due to wall thickness and mechanical strength.

The total force within a conduit is obtained by summing the steady state and waterhammer pressures in the line. Transient pressures are most important when Q is changed rapidly such as by closing a valve or stopping a pump.

The tendency to design for steady-state conditions has been common in the industry. The practice is troublesome, the pipeline may not perform as expected, it may be overdesigned and thus unnecessarily expensive. The goal is to answer how do transient arise and under what circumstances are transient conditions most severe.