3.3 Measurement of velocity and discharge



Defination


Velocity : This refers to how
quickly the water is moving. [Measured in feet
per second (ft/s).]

Discharge : discharge refers
to the water generated by the facility. It may
be dewatering water, wash water, stormwater,
or any combination of these. This term is
comparable to “flow” which is used here in
reference to receiving water flow. [Usually site
discharge is measured in gallons per minute
(gpm).


Example Of Measurement

Velocity Measurement with a Pitot Tube

For pitot tube measurements and calculations, the reference plane is taken to be at the height of the pitot tube measurements, so the equation for stagnation pressure becomes:
Pstag = P + ½ ρV2 , which can be rearranged to: V = (2ΔP/ρ)1/2
Where ΔP = Pstag – P.
The pressure difference, Δp, (or Pstag – P), can be measured directly with a pitot tube like the third U-tube in the figure above, or with a pitot tube like that shown in the figure at the right. This is a concentric pitot tube. The inner tube has a stagnation pressure opening (perpendicular to the fluid flow) and the outer tube has a static pressure opening (parallel with the fluid flow).

 

 

Example Calculation

Consider a pitot tube being used to measure air velocity in a heating duct. The air is at 85 oF and 16 psia. The pitot tube registers a pressure difference of 0.021 inches of water (Pstag – P). Calculate the velocity of the air at that point in the duct?
Solution: Convert the pressure difference of 0.021 inches of water to lb/ft2 (psf) using the conversion factor, 5.204 psf/in water.
0.021 inches of water = (0.021)(5.204) psf = 0.1093 psf
The density of air at 85oF and 16 psia can be calculated using the ideal gas law, to be 0.002468 slugs/ft3.
Now V can be calculated: V = (2ΔP/ρ)1/2 = [(2)(0.1093)/0.002468] 1/2 = 9.41 ft/se



METHODS OF DISCHARGE MEASUREMENTS

Volumetric and weight method       {Q = V/t }       {V = m/p = G/pG}
                                 
- the most precise but: only for relatively small discharges (necessary volume of tank), mainly for calibration of flow meters

Pipe flow meters based on flow contraction

=f(S2/S1,Re)


 Orifice meter


– the simplest, small laying-out length, but: large losses  

 Nozzle meter



- simpler and less expensive than a venturi meter, but not as simple as an orifice meter
  but medium losses

Venturi meter



 – more complicated shape, large laying-out length
but: small losses


Example of Calculation for Discharge (Venturi Meter)

A venturi meter is connected at the main and throat sections by tubes filled with the fluid being metered by a differential mercury manometer. Prove that for any flow the reading is unaffected by the slope of the meter.

If the mains diameter is   in. and the throat diameter   in., calculate the flow of fuel oil in gals./hr. if its relative density relative to water is 0.8 and the difference of level of the mercury columns is 7 in.
Use a direct application of Bernoulli's theorem taking the relative density of mercury to water as 13.6 and the meter coefficient as 0.96.




Applying Bernoulli:





But for a given flow   and   are constant:


                                                                                                  (3)                           

is constant

Now the pressures at level   , in the  -tube are equal and if the subscript   refers to mercury, then:
or:

(4)
From equations (3) and (4)


(5)
where  C = Constant


Now:


(6)
From equations (5) and (6) and substituting values:



From which:



Thus the flow of oil in gallons/hour



Solution


The flow of oil in gallons/hour is 4515

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