Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)

Time & Location: 2:30P - 3:20P MWF 218 MLH

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Guilichuan-gui@uiowa.edu

http://lcgui.net

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Lecture 14. Flow rate measurement

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Bulk flow rate

Flow rate measurement

- the amount of fluid that pass through a certain cross section of a pipe, duct, channel, or other conduit per unite time.

Mass flow rate

Direct methods for flow rate measurement

A

Vn - measure typical flow velocity, i.e.

𝑄=𝑉 ∙ 𝐴𝑜𝑟𝑄=∫𝐴

❑

𝑉 𝑛𝑑 𝐴

- measure amount of discharged fluid over a period of time, i.e.

�̇�=𝑚∆ 𝑡

𝑜𝑟 𝑄=𝐶∆ 𝑡 C – volume of fluid

- positive-displacement flow meters

Volume flow rate Q – usually used for liquids or low-speed gasses

- not concerned with local velocity variations across cross-section

- not concerned with short-time (turbulent) fluctuations

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Flow rate measurement

Positive-displacement (PD) flow meters

- volume flow rate calculated from the size and number of compartments and the repetition rate

- some PD meters may passively receive power from flowing fluid to operate.

- devices that isolate fixed volumes of fluid flowing into their inlet in sealed compartments and then discharge them to the outlet.

- a great variety of designs of PD meters, classified as rotary, reciprocating, or nutating

- some PD meters (metering pumps) are driven by external power source to create fluid motion.

- problems of PD flow meters: leakage and pressure loss

- PD meters for liquidsNutating disk meters, reciprocating-piston meters, rotary-piston meters, rotary-vane meters, rotor meters

- PD meters for gases

Roots-type meters, diaphragm-type meters, liquid-sealed drum-type meters

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Flow rate measurement

Nutating disk meters

- a disk rotating in a nutating fashion in a dual conical housing

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Flow rate measurement

single piston reciprocating

Reciprocating -piston meters

- plunger or piston driven by wobble plate (or cam)

77

Flow rate measurement

Rotary-piston (oscillating piston ) flow meters

- a cylindrical drum mounted eccentrically inside a cylindrical housing

88

Flow rate measurement

Rotary-vane flow meters

- flat vanes inserted into matching slots around the perimeter of a cylindrical drum located eccentrically within the housing

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Flow rate measurement

Rotor meters

Oval Gear Meters

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Flow rate measurement

Rotor meters

Gear flow meters

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Helical gear flow meter

Flow rate measurement

Rotor meters

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Flow rate measurement

Roots-type flow meters

- a particular design of a lobe meter

Lobe Rotary Piston

Flow rate measurement

Diaphragm-type meters

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Flow rate measurement

Liquid-sealed flow meters

- wet gas meters: liquid provides sealing action

Liquid ring pump

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Flow rate measurement

Restriction (or obstruction) flow meters

Venturi tubes (a & b) Flow nozzles (d) Dall tubes (c) Orifice-plate (e)

𝑑𝐷

∆ 𝑝

- Circular tube of diameter D

- Smaller diameter d in restriction to increase velocity & result in pressure drop

- Ideal volume rate determined by continuity & Bernoulli’s equation :

- Measured volume rate with empirical discharge coefficient :

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Flow rate measurement

Open-channel flow measurement

- Weirs of sharp crested and broad crested with rectangular, v-shaped or trapezoidal openings

- Flow rate over weirs:

Weirs

Venturi flumes

- converging-diverging channel constructions

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Homework

- Questions and Problems: 1 on page 219- Read textbook 9.1-9.4 on page 208 - 212

- Due on 09/30