Chapter Five Fluid Measurement

OBJECT

 At the end of this chapter the student should be able to:  Describe the importance of flow sensing and its problem  Describe the principle of operation of different flow meter  Describe the constructional and mean aspects of differential meter.

WHY IT IS IMPORTANT?

     Almost all practical fluids engineering problems are associated with the need for an accurate flow measurement, since sometimes the material transport from place to other entails payment of financial dues There is a need to measure :

local

properties (velocity, pressure, temperature, density, viscosity, turbulent intensity),

integrated

properties (mass flow and volume flow),

global

properties (visualization of the entire flow field).

WHAT WE MEASURE

 Liquid  Gases  Multiphase fluid  Solids Custody Transfer Measuring System Meter measurement system Tank measuring system Measuring system by balance

LOCAL VELOCITY MEASURMENTS

        1. Trajectory of floats or neutrally buoyant particles 2. Rotating mechanical devices

a. Cup anemometer b. Savonius rotor c. Propeller meter d. Turbine meter

3. Pitot-static tube 4. Electromagnetic current meter 5. Hot wires and hot films 6. Laser-doppler anemometer (LDA)

VOLUME-MASS MEASURMENTS

                     These devices split into two classes: mechanical instruments 1. Mass measurement

a. Weighing tanks b. Tilting traps

2. Volume measurement

a. Volume tanks b. Reciprocating pistons c. Rotating slotted rings d. Nutating disk

head-loss instruments.

1. Bernoulli-type devices

a. Thin-plate orifice b. Flow nozzle c. Venturi tube

2. Friction-loss devices

a. Capillary tube b. Porous plug

There are other widely used meters operate on different physical principles: 1. Turbine meter 2. Vortex meter 3. Ultrasonic flowmeter

TYPES OF FLOW MEASURING            The flow measurements can be classified into: Obstructive Device Differential pressure flow meter like: Venture, orifice, pitot tube Rotameter Turbines Non-obstructive Electormegnatic Ultrasonic Cross-correlation

DIFFERENTIAL PRESSURE FLOW METER  Its widely used to measure the liquid and gas  The principle is that a restriction is placed in the pipe and the differential pressure developed across the restriction is measured  The differential pressure output is calibrated in terms of volumetric flow rate (not mass this will need density)

1- ORIFICE METER  The primary element of an orifice meter is simply a flat plate containing a drilled (hole) located in a pipe perpendicular to the direction of fluid flow

Or

2- VENTURI METER

Or

        These equations for venture and orifice are valid for Turbulent flow Incompressible flow For gases : additional expansibility factor The values of discharge coeffiecient depends on Type of flow measurement; venture and orifice Diameter ratio Reynold number

CHARACTERISTICS OF DIFFERENTIAL PRESSURE MEASUREMENT         No moving parts, cheap, maintainable Well established, calibration available Permanent head loss Nonlinear relationship, so its not use for low pressure since the pressure has square root with velocity Discharge coefficient changes with wear, flow distribution Generally applicable for clean fluids Installation constraints (for straight pipe not elbow) 

COMPARISON OF VENTURE AND ORIFICE Venturi Expensive but offer good accuracy Long working life and almost no maintenance Can measure flow for fluid with suspended solid High rang Lowest permanent head loss orifice Least expensive Low working life due to wear in the edge Used for clean fluid, can be used for dilute slurries

3- PITOT TUBE

  The Pitot tube is used to measure

the local velocity

at a given point in the flow stream and not the average velocity in the pipe or conduit. One tube,

the impact tube

, has its opening normal to the direction of flow and

the static tube

has its opening parallel to the direction of flow.

  The fluid flows into the opening at point 2, pressure builds up, and then remains stationary at this point, called “

Stagnation Point

”. The difference in the

stagnation pressure

(impact pressure) at this point (2) and the static pressure measured by the static tube represents the pressure rise associated with the direction of the fluid. Impact pressure head = Static pressure head + kinetic energy head  where, Cp: dimensionless coefficient to take into account deviations from Bernoulli’s equation and general varies between about 0.98 to 1.0.

 The first method, the velocity is measured at the exact center of the tube to obtain umax. then by using the Figure, the average velocity can be obtained.  The second method, readings are taken at several known positions in the pipe cross section and then a graphical or numerical integration is performed to obtain the average velocity, from the following equation;

4 - THE NOZZLE  The nozzle is similar to the orifice meter other than that it has a

converging tube

in place of the orifice plate, as shown in below. The velocity of the fluid is gradually increased and the contours are so designed that almost frictionless flow takes place in the converging portion; the outlet corresponds to the the upstream pressure alone.

vena contracta

on the orifice meter. When the ratio of the pressure at the nozzle exit to the upstream pressure is less than the critical pressure ratio ωc, the flow rate is independent of the downstream pressure and can be calculated from 

Nozzle Expensive Long working life and almost no maintenance Generally Used to measure steam High discharge coefficient = 0.99

It has permanent head loss orifice Least expensive Low working life due to wear in the edge Used for clean fluid, can be used for dilute slurries Low discharge coefficient= 0.62

The same permanent head loss since it has no diverging cone

5 VARIABLE AREA METERS – ROTAMETERS

    In the Rotameter

the drop in pressure is

constant and

the flow rate is function of the area of constriction

. When the fluid is flowing the float rises until its weight is balanced by the up thrust of the fluid.

Force balance on the float Gravity force = up thrust force +(drag force)Pressure forec Vf ρf g = Vf ρg + (–ΔP) Af   A1 : cross-section area of the tube when the float arrived.

A2 : cross-section area of the annulus (flow area).

EXAMPLES

 1- A horizontal Venturi meter is used to measure the flow rate of water through the piping system of 20 cm I.D, where the diameter of throat in the meter is d2 = 10 cm. The pressure at inlet is 17.658 N/cm 2 gauge and the vacuum pressure of 35 cm Hg at throat. Find the discharge of water. Take Cd = 0.98.

 2- A Venturi meter is to be fitted to a 25 cm diameter pipe, in which the maximum flow is 7200 lit/min and the pressure head is 6 m of water. What is the maximum diameter of throat, so that there is non negative head on it?

   3- A (30cm x 15cm) Venturi meter is provided in a vertical pipe-line carrying oil of sp.gr. = 0.9. The flow being upwards and the difference in elevations of throat section and entrance section of the venture meter is 30 cm. The differential U-tube mercury manometer shows a gauge deflection of 25 cm. Take Cd = 0.98 and calculate: i-The discharge of oil Ii-The pressure difference between the entrance and throat sections.

EXAMPLES

 4- An orifice meter consisting of 10 cm diameter orifice in a 25 cm diameter pipe has Cd = 0.65. The pipe delivers oil of sp.gr. = 0.8. The pressure difference on the two sides of the orifice plate is measured by mercury oil differential manometer. If the differential gauge is 80 cm Hg, find the rate of flow.

 5- Water flow through an orifice meter of 25 mm diameter situated in a 75 mm diameter pipe at a rate of 300 cm 3 /s, what will be the difference in pressure head across the meter μ = 1.0 mPa.s.

 6- Water flow at between 3000-4000 cm3/s through a 75 mm diameter pipe and is metered by means of an orifice. Suggest a suitable size of orifice if the pressure difference is to be measured with a simple water manometer. What approximately is the pressure difference recorded at the maximum flow rate? Cd = 0.6.

EXAMPLES

 7- A rotameter tube of 0.3 m long with an internal diameter of 25 mm at the top and 20 mm at the bottom. The diameter of float is 20 mm, its sp.gr. is 4.8 and its volume is 6 cm3. If the coefficient of discharge is 0.7, what will be the flow rate water when the float is half way up the tube?

 8- A Pitot tube is inserted in the pipe of 30 cm I.D. The static pressure head is 10 cm Hg vacuum, and the stagnation pressure at center of the pipe is 0.981 N/cm 2 gauge. Calculate the discharge of water through the pipe if u/u max = 0.85. Take Cp = 0.98.

   9- A Pitot tube is placed at a center of a 30 cm I.D. pipe line has one orifice pointing upstream and other perpendicular to it. The mean velocity in the pipe is 0.84 of the center velocity (i.e. u/ux =0.94). Find the discharge through the pipe if: i-The fluid flow through the pipe is water and the pressure difference between orifice is 6 cm H2O.

Ii-The fluid flow through the pipe is oil of sp.gr. = 0.78 and the reading manometer is 6 cm H2O. Take Cp = 0.98.

6- THE NOTCH OR WEIR

  It is an obstruction in the channel that causes the liquid to back up behind it and to flow over it or through it. By measuring the height of upstream water surface, the rate of flow is determined. The velocity with which the liquid leaves depends on its initial depth below the surface.

Many shapes of notch are available of which three shapes are given here as follows, 6-1 Rectangular Notch To prove this equation applies Bernoulli’s equation between points M and N as shown in Figure;  The cross sectional area of flow at point M is larger than that at notch (point N), then (uM ≈ 0) PM = PN = Po atmospheric pressure The discharge will be:

6- THE NOTCH OR WEIR

 6-2 Triangular Notch  A triangular notch is also called a

V-notch.

    H: height of liquid above base of the apex of the notch.

θ: Angle of the notch.

tan (θ/2) = x / H = x' / (H-h) The width of the notch at liquid surface = 2x = 2H tan(θ/2)    The width of the strip = 2x' = 2(H-h) tan(θ/2) The area of the strip = 2x' dh = 2(H-h) tan(θ/2)dh The discharge is:

6- THE NOTCH OR WEIR

 6-3 Trapezoidal Notch  A trapezoidal notch is a combination of a rectangular notch and triangular notch as shown in Figure;  Discharge over the trapezoidal notch, Q=[Discharge over the rectangular notch + Discharge over the triangular notch]  The discharge is

EXAMPLES

 10- A rectangular notch has a discharge of 21.5 m3/min, when the head of water is half the length of the notch. Find the length of the notch where Cd = 0.6.

 11- A rectangular channel 1.5 m wide is used to carry 0.2 m3/s water. The rate of flow is measured by placing a 90º V notch weir. If the maximum depth of water is not to exceed 1.2 m, find the position of the apex of the notch from the bed of channel. Cd = 0.6.

 12- A trapezoidal notch 120 cm wide at top and 45 cm at the bottom has 30 cm height. Find the discharge through the notch, if the head of water is 22.5 cm. Cd1 = Cd2 = 0.6.

NON-OBSTRACTIVE DEVICES

   Ultrasonic flowmeters. Two examples are shown. The pulse-type flowmeter. Upstream piezoelectric transducer A is excited with a short sonic pulse which propagates across the flow to downstream transducer B. The arrival at B triggers another pulse to be created at A, resulting in a regular pulse frequency f The same process is duplicated in the reverse direction from

B to A, creating frequency

. The is proportional to the flow rate. The

doppler type arrangement, where sound waves from transmitter T are scattered by particles or contaminants in the flow to receiver R. Comparison of the two signals reveals a doppler frequency shift which is proportional to the flow rate. Ultrasonic meters are nonintrusive and can be directly attached to pipe flows in the field . Their quoted uncertainty of 1 to 2 percent can rise to 5 percent or more due to irregularities in velocity profile, fluid temperature, or Reynolds number.

  Hot-wire anemometer. A very fine wire (

d 0.01 mm or less) heated between two small probes, It is ideally suited to measure rapidly fluctuating flows such as the turbulent boundary layer. The idea dates back to work by L. V. King in 1914 on heat loss from long thin cylinders. If electric power is supplied to heat the cylinder, the loss varies with flow velocity across the cylinder according to King’s law

Because of its frailty, the hot wire is not suited to liquid flows, whose high density and entrained sediment will knock the wire right off. A more stable yet quite sensitive alternative for liquid-flow measurement is the hot-film anemometer .

A thin metallic film, usually platinum, is plated onto a relatively thick support which can be a wedge, a cone, or a cylinder.

        Laser-doppler anemometer. In the LDA a laser beam provides highly focused, coherent monochromatic light which is passed through the flow. When this light is scattered from a moving particle in the flow, a stationary observer can detect a change, or

doppler shift, in the frequency of the scattered light. The shift f is proportional to the velocity of the particle. There is essentially zero disturbance of the flow by the laser.

The advantages of the LDA are as follows: No disturbance of the flow High spatial resolution of the flow field Velocity data that are independent of the fluid thermodynamic properties An output voltage that is linear with velocity No need for calibration The disadvantages are that both the apparatus and the fluid must be transparent to light and that the cost is high