GROUP 1

2.10-C PRESSURE DROP and FRICTION FACTOR in TURBULENT FLOWBy: Group 1ZabanalCarriedoFernandezIgnacioPagaduanMartinezMontes Turbulent flow vs Laminar FlowLaminar flow:Where the fluid moves slowly in layers in a pipe, without much mixing among the layers. Typically occurs when the velocity is low or the fluid is very viscous.

Turbulent flow vs Laminar FlowTurbulent flowOpposite of laminar, where considerable mixing occurs. Velocities are high.

Turbulent flow vs Laminar Flow

Turbulent flow vs Laminar FlowLaminar and Turbulent flows can be characterized and quantified using Reynolds Number established by Osborne Reynoldsand is given as where

= Viscosity of liquid Pa s

= Density of liquid kg / m 3V = Flow Velocity m/sD = Diameter of the pipe mm = mass flow rate kg /seco

Turbulent flow vs Laminar FlowNOTE Reynolds number directly proportional to velocity & inversely proportional to viscosity!

NR < 2000 laminar flowNR > 4000 Turbulent flowFor 2000 < NR < 4000 transition region or critical region flow can either be laminar of turbulent difficult to pin down exactly.Pressure DropWhen fluid flows through a pipe there will be a pressure drop that occurs as a result of resistance to flow. There may also be a pressure gain/loss due a change in elevation between the start and end of the pipe.

Mechanical Energy loss/ Friction lossFriction lossis the loss of energy or head that occurs in pipe flow due to viscous effects generated by the surface of the pipe.Friction Loss is considered as a "major loss" and it is not to be confused with minor loss, which includes energy lost due to obstructions. In mechanical systems such asinternal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces.This energy drop is dependent on the wallshear stress() between the fluid and pipe surface. The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. For turbulent flow, the pressure drop is dependent on the roughness of the surface. In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent.

Mechanical Energy loss

9Fanning friction factorFanning friction factor- TheFanning friction factor, named after John Thomas Fanning (18371911), is adimensionless numberused in fluid flow calculations. It is related to theshear stress at the wall as:

Fanning friction factor

Fanning friction factor

NOTE: AS THE REYNOLDS NUMBER INCREASES, THE FRICTION FACTOR DECREASES. And THE RAT E OF DECREASE BECOMES SMALLER FOR GREATER RELATIVE FACTORS. H. Darcy

Fanning friction factor

Fanning friction factor

Determining Fanning Friction Factor in turbulent flowUse of Moody Chart

Determining Fanning friction factor in Turbulent FlowUse of Zigrang-Sylvester Equation and Haaland Equation.

In these equations, is the Reynolds number and is the relative roughness. The textbook by Welty et al. lists the Haaland Equation as an alternative to the Colebrook Equation for explicit calculation of the friction factor when the Reynolds number and the relative roughness are specifiedDetermining Fanning friction factor in Turbulent Flow

The Zigrang-Sylvester Equation, which also permits explicit calculation of the friction factor when the Reynolds number and the relative roughness are specified, performs somewhat better than the Haaland Equation in approximating the Colebrook result over a wide range of values of both the Reynolds number and the relative roughness. Therefore it is recommended for your use when such explicit calculation is desired.The Roughness coefficients of pipes

The Pipe Values

The Pipe Values

Example 2.10-3 use friction factor in turbulent flow

A liquid is flowing through a horizontal straight commercial steel pipe at 4.57m/s. The pipe used is commercial steel, schedule 40, 2in nominal diameter. The viscosity of the liquid is 4.46cp and the density 801 kg/m3. Calculate the mechanical-energy friction loss Ff in j/kg for a 36.6m section of the pipe.Solution:From Appendix A.5, D=0.525mV=4.57m/s= 801 kg/mL=36.6m

Flow is turbulent. The equivalent roughness is 4.6x10-5

22 determining the Fanning Friction Factor:Using the Moody graphCalculating the value directly from any of the equations: Colebrook equation, Zigrang-Sylvester Equation,And Haaland equation

Use of Zigrang-Sylvester Equation

Thus, solving for the friction loss

2.10-3 Frictional loss in straight pipe and effect of type of pipeA liquid having a density of 801 kg/m3 and a viscosity of 1.49x10-3 pa.s is flowing through horizontal straight pipe at a velocity of 4.57m/s. the commercial steel pipe is 1 in nominal pipe size, schedule 40. for a velocity of 4.57m/s. , do as follows:a.) calculate the friction loss Ffb.) for a smooth tube of the same inside diameter, calculate the friction loss. What is the percent reduction of the Ff for the smooth tube?27Solution:Given: density of 801 kg/m3 velocity of 4.57m/s. viscosity of 1.49x10-3 pa.s velocity of 4.57m/s. diameter= 0.04089 m(Appendix 5)roughness factor= 4.6 x 10-5 m

Solution:Solving for Reynolds number:

Solution:Solving for the relative roughness factor:

Solution:

Solution:

Where relative roughness=0.001125 and Re=1.00456x10^6f= 0.0055 rough pipef= 0.004 (smooth pipe) accdng to the moody chart presented on the next slideAnd accdng to the equation:(f=0.79/(1.0045x10^5)^0.25)

Solution

Solution:A.)

B.)

SolutionPercentage loss= 100%-(249.25/320.48*100%)=22.17%