Flow Meter Viewgraphs

FLOW METER LAB

BACKGROUND

Direct & Indirect Measures

Direct methods measure the quantity (volume or weight)

for a given time interval

Indirect methods measure pressure change, etc, that can

be related to flow rate

Constriction Meters (Indirect Methods)

Pressure Change For Flow Area Change

Bernoulli equation (ignoring head loss)

v_i = Q/A_i h_i = p_i/γ + z_i

Empirical equation

Q=KA₀(2g Δh)^0.5

A₀ can be A₁ or A₂

(Just slightly different K values
K also adjusts for energy losses in real world)

Chart From ROBERSON & CROWE, Chapter 13

K vs Re for various constriction meters

PROCEDURES

       Use the smaller water supply pump

      Orifice, Venturi, or Nozzle Meter
            Different for each team
            Valve before meter should be wide open
            Control flow with valve following meter

      Issues To Consider On Data
             What limits precision?
              Can you control it?

       Compare The Three Meters
              Can you see any visual difference?

Data Required

We want to get Q, Δh, & A₀

Gravimetric flow measurement

Q = ΔV/ Δt = (W₂-W₁)/ γ(t₂-t₁)

Density (γ) is tabulated vs temperature

Measure weight (W) & time (t)

Differential head

Manometer readings: h₁ & h₂

Δh = h₁ - h₂

Circular pipe area

A = πD²/4

There are two diameters, but we use only one in A

Other goes into K

We know diameters of venturi, nozzle, & orifice

Pipe size interesting, but not required

Summarize Data Required

- W₁, W₂, t₁, t₂, and water temperature (t₁ may be zero)

- Heads for two sides of differential manometer

(Average over Δt?)

- For 5-10 runs (to plot Q vs Δh)

FLOW METER LAB RESULTS

   Review
        Venturi, nozzle and orifice meters

        Experimental Data
           Weights (lb)
           Time (sec)
           Head (in)
           Temperature (°F) [minor]

DATA NEEDED IN RESULTS

   Δh (ft), Q (cfs), K, Re

      Δh (ft) = (H₁-H₂) (in)/12 (in/ft)

       Q (cfs) = ((W₂-W₁) (lb)/62.4 (lb/ft³))/(t₂-t₁) (sec)

    Dimensionless variables K & Re
        K = Q(cfs)/((πD²/4) (ft²)(64.4(ft/sec²)Δh(ft))^0.5)
        Re = vD/ν = 4Q(cfs)/πD(ft)ν(ft²/sec)

RESULTS REQUESTED

        Tabulated Data Above

        Graphs: Q(cfs) vs Δh (log-log scale)
                       K vs Re
           Compare with graphs in literature

        Fit Equation Q = KA(2g Δh)^x
           Δh Constrained (x = 0.5)
           Δh Unconstrained (x free)

Example Flow Meter Data

[Here are two examples of how data might be presented]

               CONSTANT DATA
    Water Temperature    76 F
    Water Spec. Wt. 62.37 lb/ft^3
    Kinem.Visc.         1.03 x 10^-5 ft^2/s
    Pipe Diameter 2 in.
    Orifice Diameter 1.2 in.

VARIABLE DATA

Manometer

Weights

Times

H1	H2	Start	End	Start	End
(in)	(in)	(lbf)	(lbf)	(sec)	(sec)
-29.2	32.2	420	820	0	78
-23.0	25.3	380	780	0	79
-21.5	24.5	600	1000	0	80
-17.0	19.1	360	760	0	97
-16.25	18.5	240	640	0	91
-11.0	12.3	1080	1480	0	111
- 4.8	5.3	600	1000	0	169

Calculated Results

   Date of Calculation: Feb 17, 2005
    Nozzle/Pipe Diam. Ratio (Beta) = 0.6
    Nozzle Area = 1.14 sq. in.

      Delta H     Flow Rates       K           Re
           (ft)       (lb/s)    (cfs)
       5.117       5.128 0.0822 0.577 1.016x10^5
       4.025       5.063 0.0812 0.642 1.004
       3.833       5.000 0.0802 0.650 0.991
       3.008       4.124 0.0661 0.605 0.817
       2.896       4.396 0.0705 0.657 0.871
       1.942       3.604 0.0578 0.658 0.714
       0.842       2.367 0.0379 0.656 0.469