PIPE FLOW: TURBULENT

BACKGROUND

            Smooth & rough pipes:

                Qualitative rating of pipe surface

            Relative roughness:

                Average roughness along pipe divided by

                        pipe diameter

        Static heads:

                Measured perpendicular to direction of flow:

                        (p/γ + z)

        Stagnation head:

                Tap pointed up-stream of flow direction:

                        (p/γ + z + v²/2g)

            Laminar & turbulent flow

                        Some theory for laminar flow

                        Civil Engineers almost always work with

                        turbulent flow for pipes

  Hydraulic Grade Line In A Pipe

           Energy Equation for Steady, Uniform Flow

                        p₁/γ + z₁ + v₁² + h_P = p₂/γ + z₂ + v₂² + + h_T + h_L

     Subscripts 1 & 2 are at the start and end of the flow section

   h_L is the head loss due to flow over a length of the pipe from points 1 & 2

     h_P and h_T are heads associated with pumps and turbines respectively

           Common Headloss Equations

      Darcy-Weisbachh_L = f (L/D) (v²/2g)

      Hazen-Williams h_L = (v/αC)^1.85L/R^1.17

      Manning: h_L = (nv/β)² L/R^4/3

R is hydraulic radius; f and n are resistance factors, and C is a conductivity factor. α and β are needed to convert for common units.

TURBULENT FLOW IN PIPES

Objectives:

To determine the friction factors associated with turbulent flow in smooth and rough pipes.

To observe and compare the velocity distributions in smooth and rough pipes.

Apparatus:

Pipe assemblies equipped with taps and a manometer board

Upstream orifice meter with differential manometer

Movable stagnation tubes and manometers fitted to the outlets of the pipes

Pipe Flow Apparatus

 Pipe assemblies equipped with taps and a manometer

         board

 Upstream orifice meter with differential manometer

 Movable stagnation tubes and manometers fitted to the

         outlets of the pipes

Experimental Procedure

1. Set up the experiment.

       a.    Open the surge tank valve and turn on the small pump.

Release water from several valves around the lab to remove air from the piping system.

       b.    Measure the positions of the manometer taps along the two pipes.

       c.    Measure the water temperature

2.    Measure head loss vs. distance and flow.

       a.    Establish a steady flow through one of the pipes

       b.    Use the back-pressure valve at the end of the pipe to control the level of the manometers

       c.    Record the levels for all manometers

       d.    Record the differential head across the orifice in the supply line

       e.    Convert the orifice manometer reading to flow using the rating curve provided

3. Repeat Step 2 for 6-7 flows through the subject pipe

4. Measure the velocity profile across the pipe.

5. Repeat Steps 2, 3, and 4 for the second pipe.

6. Turn off the pump and drain the pipes. Close the

          surge tank valve.

Data Sheet for Turbulent Flow (1)

Calif. State Univ., Sacramento                                                CE 135 HYDRAULICS LAB.

Dept. of Civil Engineering

TURBULENT FLOW IN PIPES

INPUT (OBSERVED) DATA

Lab. Team:                                                                             Date of Experiment: 

------------------------------------ CONSTANT DATA ----------------------------------------------

Water Temperature ________° F

----------------------------------- VARIABLE DATA ------------------------------------------------

PIPE TYPE: _____________________ PIPE D(in) = ________

            FLOW HEAD                        MANOMETER HEADS (in)

  1                                  H->

      Flow           Gpm (H-ref->) 

  2                                  H->

      Flow 

  3                                  H->

      Flow 

  4                                  H->

      Flow 

  5                                  H->

      Flow 

  6                                  H->

      Flow 

  7                                  H->

      Flow 

Reference Tap “H-ref”

                            (Optional)

Purpose: Adjust for effect of random pressure (head)

        fluctuations in the pipes

Assign one of the taps, say the one at X=0, to be read at

       the same time as H is read for each tap at a point

       at distance 0-18.5

If both fluctuate at same time, the two points get same

       change

(Not perfect, but helps)

Experimental Results (1)

Plot the piezometric head vs. pipe pressure tap position

       for all flow rates and pipes.

These are used to determine the head loss - length relationship

Determine the relative roughness (k_s/D)

Calculate friction factor (f) and Reynolds Number (Re)

Plot your f and Re data on a Moody diagram.

      Determine the relative roughness of each pipe

      Calculate the absolute roughness.

Plot a graph, at log-log scale, of f vs. Re, like the Moody

       diagram

Flow From Velocity Distribution

Theoretical Equation: Q = ∫v2πrdr = 2π∫vrdr

Ideally, v is constant around the circular path at radius r. In practice, some variation can be expected.

Practical Equation: Q = ∑ v_i ΔA = ∑ v_i 2πr_i Δr

Data Sheet for Turbulent Flow (2)

Velocity Profile Data

Velocity Distribution Data: Manometer # ______

          Heads for Flow: H1 ______ in  H2 ______ in [Gives Q = ________ cfs]

Reading Number    1       2      3      4      5      6      7      8      9

Probe Location:

      (Inch)

Stagnation Head:

      (Inch)

Static Head:

      (Inch)

Experimental Results (2)

Calculate values of Hazen-Williams coefficient for each

run. How good is the assumption that the coefficient is constant with Re?

Compare your measurements of absolute roughness and

Hazen-Williams coefficient with tabulated values for copper and galvanized steel pipe

Note:

       Re = vD/ν = 4Q/πDν

       f = 2gDh_L/Lv² = g π²D⁵h_L/8LQ²

       Hazen-Williams C = v(L/h_L)^0.54/0.355D^0.54

Example Spreadsheet Data

CONSTANT DATA

          Water Temp. 75    F       Spec. Wt. 62.37 lb/ft^3 

                                         Kinem.Visc. 1.03 x 10^-5 ft^2/s

VARIABLE DATA

   ------------------------ Copper Pipe ------ D(in)=      2.004 ---------------------------

   ------- Flow Rate -------  ------------- Manometer Heads (inches) ------------

CE 135 HYDRAULICS LAB.     FLOW IN PIPES WITH FRICTION

CALCULATIONS

         COPPER (SMOOTH) PIPE

Darcy-Weisbach and Hazen-Williams Coefficients

Run  Reynolds        Darcy-    Hazen-    

No.  Number         Weisbach Williams   Epsilon

                                    f              C          (ft)

 1     0.0799 x10^6    0.0199      148        0.0375 x 10^-3

 2     0.1034               0.0190      148        0.0366

 3     0.1151               0.0171      155        0.0103   

 4     0.1218               0.0177      152        0.0130   

 5     0.0331               0.0239      143        0.0566 

 6     0.0641               0.0204      148        0.0251

Roughness values computed from Colebrook equation:

        Absolute Roughness = 0.0232 x 10^-3 ft

        Relative Roughness = 0.139 x 10^-3