Physics Chapter on Force Measurement

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Questions and Answers

What is the SI unit of force?

Pound-force (lbf)

Pascal (Pa)

Newton (N) (correct)

Kilogram (kg)

How is weight defined in terms of mass and gravity?

Weight = mass × force

Weight = mass × acceleration

Weight = mass × gravity (correct)

Weight = mass × velocity

Which method involves measuring the deflection caused by an unknown force?

Standard Method

Direct Method

Indirect Method (correct)

Comparative Method

What is a characteristic of the direct method of force measurement?

It compares an unknown force with a known gravitational force. (B) Signup and view all the answers

Which formula correctly represents Newton's second law of motion?

Force = Mass × Acceleration (D) Signup and view all the answers

Which of the following is an indirect method for measuring force?

Measurement of deflection on a calibrated scale (C) Signup and view all the answers

What does the gravitational force (g) equal in m/s² on Earth?

9.81 m/s² (D) Signup and view all the answers

Which method translates an unknown force into fluid pressure?

Hydraulic and pneumatic load cells (C) Signup and view all the answers

What does the frequency shift in sound waves due to the Doppler effect indicate in flow measurements?

The average flow velocity in the pipe (B) Signup and view all the answers

Which equation can be used to estimate the volume flow rate for an obstruction flow meter?

Q ~ SQRT(P1 - P2) (B) Signup and view all the answers

What is one significant advantage of ultrasonic flow meters?

They have no moving parts (A) Signup and view all the answers

What is a major limitation of ultrasonic flow meters?

Sensitivity to dirt and impurities in the fluid (C) Signup and view all the answers

In a positive-displacement flow meter, what is measured to determine flow rate?

The number of discharges per unit time (B) Signup and view all the answers

Why are positive-displacement flow meters suitable for high viscosity liquids?

They minimize fluid slippage between chambers (C) Signup and view all the answers

Which flow measurement method uses the principle of transit time to calculate flow rate?

Ultrasonic flow meter (A) Signup and view all the answers

What is a key characteristic of laminar flow meters?

They relate flow rate to pressure difference (B) Signup and view all the answers

What is one significant advantage of positive-displacement flow meters?

Suitable for low flow rates (A) Signup and view all the answers

Which of the following is a limitation of positive-displacement flow meters?

They create large permanent pressure drops downstream (D) Signup and view all the answers

What is the primary purpose of flow meter calibration?

To compare flow meter measurements to a standard (C) Signup and view all the answers

Which type of flow meter is known for having no moving parts?

Vortex-shedding flow meter (B) Signup and view all the answers

In which scenario are positive-displacement flow meters typically used?

In utility measurements such as gas and water at home (B) Signup and view all the answers

What does the parameter $Q$ represent in fluid flow meters?

Flow rate (B) Signup and view all the answers

Which equation is associated with the flow nozzle in obstruction flow meters?

$Q ~ SQRT (P1-P2)$ (D) Signup and view all the answers

The measurement of discrete fluid flows (m3) instead of a flow rate (m3/s) indicates what about positive-displacement flow meters?

They are limited in their application for measuring rates (B) Signup and view all the answers

What is a common characteristic of laminar flow meters in terms of flow rate?

They provide a direct reading of flow rate (A) Signup and view all the answers

Which of the following is a key feature of negative impacts regarding dirty fluids for positive-displacement flow meters?

They require disassembly and cleaning when polluted (C) Signup and view all the answers

Study Notes

Force, Torque, and Power Measurements

Force is a vector quantity, having both magnitude and direction
A force can accelerate or decelerate an object by pulling or pushing it
Force equals mass times acceleration (F = ma)
Weight is the measure of the force of gravity acting on an object
Weight (w) = mass (m) x gravity (g)
The SI unit of force is the Newton (N)
The British unit of force is the pound-force (lbf)
1 N = 1 kg⋅m/s² ≈ 0.225 lbf
1 lbf = 4.448 N

Force Measurement Methods

Direct Method: Directly comparing a force to a known force, using a physical balance.
Indirect Method: Measuring the effect of a force on an elastic element (like a spring) and calculating the force from the measured deflection.

Methods for Force Measurement

Balance/Scales: Using a known mass's gravitational force to balance the unknown force.
Elastic Member: Applying the force to a calibrated spring, beam, or cantilever and measuring the resulting deflection.
Capacitor/Piezoelectric Transducer: Using a capacitor or piezoelectric transducer to measure the change in capacitance/charge due to force application.
Fluid Pressure: Translating the force into fluid pressure and measuring the resultant pressure with load cells (hydraulic or pneumatic).
Acceleration: Applying the unknown force to a known mass and measuring the resulting acceleration.
Magnet/Coil: Balancing the unknown force against a magnetic force generated by a magnet and current in a coil.

Equal-Arm Beam Balance

Measures the mass or weight of an object
The force of known weights equal the unknown object's weight when the beam is horizontal
Calibration can be for force or mass units, depending on the scale type.

Unequal-Arm Beam Balance

W₁b = W₂a, where W₁ and W₂ are the weights, 'b' and 'a' are the distances from the fulcrum
The unknown weight is computed using this equation

Sources of Errors in Balance Scales

Errors in reference weights
Misaligned components (thermal expansion/contraction)
Buoyancy (air displacement)
Friction inaccuracies
Condensation/evaporation of water
Chemical reactions/corrosion
Vibration and air gusts

Spring Scale

Operates based on Hooke's Law: F = kx (force = spring constant x displacement)
The force reading applies to constant acceleration frames, like Earth
The readings are not true in accelerating/decelerating environments like elevators.

Strain-Gauge Load Cell

Uses a Wheatstone bridge configuration with four strain gauges to measure force
Change in resistance due to applied force leads to a measurable output
Must operate within elastic range
Requires calibration

LVDT Load Cell

Measures displacement of an elastic diaphragm
LVDT produces a voltage proportional to the force
The device itself can measure pressure or acceleration besides force
Operates within the elastic range

Proving Rings

Known physical dimensions and mechanical properties used for calibrations
An external tensile or compressive force causes the ring to deform proportionally
A displacement sensor measures the deflection related to the applied force.

Capacitive Load Cells

Stores charge using two flat plates
The capacitance is proportional to the distance between the plates.
A change in distance due to applied pressure causes a change in capacitance
Change in capacitance translates to weight calculations

Piezoelectric Force Transducer

Piezoelectric materials generate a charge when deformed by an applied force
The generated charge is proportional to the applied force's magnitude

Force to Fluid Pressure Conversion

Force on a piston or diaphragm inside a fluid directly translates into pressure
The fluid pressure is proportional to the applied force
Pneumatic/hydraulic load cells translate applied force to pressure, providing a measurable output

Pneumatic/Hydraulic Load Cells

Used primarily for wide range measurements of force
Force causes a proportional change in the fluid pressure within the device
Cells must operate within the elastic range
Calibration is required to relate applied force with output pressure (or electric signals)
The generated pressure can be converted into an electric signal
The cell is unaffected by transient voltages, like lightning surges, when no electric components are present

Accuracy of Different Load Cells

Accuracy and sensitivity vary among capacitive, strain-gauge, pneumatic, and hydraulic load cells.

Torque Measurements

Torque is the rotational effect of a force
Torque = force x perpendicular distance from the force's line of action to the axis of rotation (T = r x F)
Torque is a vector quantity.

Torque Versus Brake Power

Brake power (P) = Torque (T) x angular velocity (ω)/60, where ω is expressed in RPM.
The torque exists even in the absence of rotation
The formula of brake power equals zero at zero RPM.

Torque Meters

Measures torque in a rotating system (engine, shaft, gearbox)
Primarily categorized as rotary or reaction (static/non-rotational) type sensors.
Static torque is usually easier to measure than dynamic torque.
Reaction sensors are often less complex, hence less expensive, than rotary sensors for static torque measurements.

Reaction Torque Meters

Commonly use a flange-to-flange sensor setup.
Rotation generates shear forces.
Foil strain gauges measure these shear forces and voltage is created by a Wheatstone bridge.
Measurements are taken on elastic members, yielding the deflection/strain and the applied torque.
Commonly used as calibration tools.

Measurements of Brake Power

A dynamometer measures the brake power
One horsepower is equivalent to 735 Watts.
1 Watt= 1 Joule/sec (work done per unit time)

Dynamometers

Devices to measure the power output by a rotating device
Classified into two types: absorption and driving
Absorption: Measures power output by converting it into heat
Driving: Measures power that is delivered to the tested device

Careful with the Inlet Air Temperature and Pressure

The measured brake power is proportional to the inlet air density.
Inlet air density affects the result of measured brake power

Prony Brake Dynamometer

A simple dynamometer to measure brake power output
Converts brake energy into heat using dry friction
Attempts to stop the engine/rotating device by measuring the weight that the brake supports.

Hydraulic Dynamometer

A method for measuring a rotating device's brake power.
Uses water/cooling fluid for conversion to measure torque and power produced.
Consists of a casing that rotates around the input shaft.
Measures the torque and thus brake power output.

Eddy Current Dynamometer

Measures torque and output power created by an electromagnetic field.
Uses a rotor that is rotated in a magnetic field.
Eddy currents in the rotor created by the field slow the rotor, allowing for determination of the torque.

Measurements of RPM

RPM determination typically involves either mechanical coupling, or non-contacting optical methods.
The frequency of sensed interruptions is directly proportional to the rotational rate, or rpm.

Mechanical Devices: Tachometers

Attached to rotating shafts via mechanical coupling or friction
Employs a dc permanent-magnet generator which provides a voltage directly proportional to the rotational speed.
May be attached permanently, or connected via friction, to continuous monitoring.

Non-Contact Optical RPM Meter: (a) LED Photo Detector Wheel

Measures the rotational speed by use of a rotating shaft with openings
The frequency of light interruption (beam to wheel) is proportionate to the rpm.
Measures the interruption frequency, related to the rotational rate or rpm

Non-Contact Optical RPM Meter: (b) Stroboscope

Measures rotational speed by use of a flashing strobe light.
The flashing frequency coincides with the object/shaft's rotational speed
This allows determination of the angular speed

Flow Rate Measurements

Several methods exist to measure fluid flow rate.
Obstruction Flow Meters: (Orifice Meter, Flow Nozzle, and Venturi Meter) use flow restrictions and pressure differences to estimate the flow rate.
Laminar Flow Meters: measure flow rate based on the Hagen-Poiseuille equation, which applies to laminar fluid flow through a constant cross-section tube.
Variable-Area Flow Meters (Rotameters): use a float within a tapered tube to visually measure flow rate.
Turbine Flow Meters: Use a spinning turbine wheel to calculate flow rate, based on rotational speed proportionality.
Vortex-Shedding Flow Meters: Calculate flow rate based on periodic shedding of vortices.
Ultrasonic Flow Meters: Use transit time or Doppler effect of sound waves to measure flow.
Positive-Displacement Flow Meters: Count the times units of a fixed volume are repeatedly discharged to get the total volume of fluid flow rate in unit time

Vortex Shedding

Vortex shedding occurs when a fluid passes over a bluff body.
The shedding frequency is directly proportionate to the velocity of the resulting fluid flow.

Strouhal Number

A non-dimensional number used in vortex shedding studies.
It relates the vortex-shedding frequency (f), characteristic dimension of the bluff body (d), and the mean velocity (V)

Flow Meters: Vortex-Shedding Meters

Use vortex shedding phenomena to determine the flow rate.
The frequency of vortices cast is proportionate to the flow velocity.

Flow Meters: Paddle Flow Meters

Similar in use to turbine flow meters but doesn't obstruct the entire cross-section of the flow
It has lower sensitivity in comparison with turbine meters.

Flow Meters: Turbine Flow Meters

Calculate fluid flow rate by measuring the rotational speed of a turbine wheel that turns proportional to the fluid velocity through the pipe
Measures flow accurately, with a low margin of error

Ultrasound Flow Meters

Use sound waves to measure fluid flow and use either time of travel or Doppler effect
Time of travel considers the difference of travel time between upstream transmitter and downstream receiver
Doppler effect considers the alteration in the frequency of reflected sound waves to estimate flow rate

Positive-Displacement Flow Meters

Measures flow by counting the units of a fixed volume repeatedly discharged in a given period
This is how the total volume flow is determined
Suitable for high viscosity fluids.
The fixed volume chamber will change in relation to the flow
Provides a direct reading of the flow and is useful for liquids and gases

Flow Meter Selection Criteria

Table demonstrating which flow meter is suitable according to different criteria like accuracy, repeatability, and cost.

Flow Meters: Calibration

Accurate calibration requires setting up leak-free connections for testing devices and creating steady state flow
The appropriate standards need to be used during the calibration process

Fluid Velocity Measurements

Velocity includes magnitude and direction.
Speed is a scalar which is of only magnitude.
Two measurement methods are used interchangeably: anemometry and velocimetry

Pitot-Static Tubes

A two-holed tube measures the velocity of incompressible fluids at a point
Measures the static and total fluid pressure, using a static pressure port at the same physical location.
Calculation of dynamic pressure using difference between total and static pressures.

Pitot-Static Tubes: Compressibility Effects

The formula for calculating total or stagnation pressure is revised to account for compressible effects.
The Mach number (M) is a crucial factor to consider in the equation when dealing with compressible flows.

Pitot-Static Tubes: Stagnation Pressure

The stagnation or total pressure is measured when velocity is zero (no motion)
The fluid is brought to rest via isentropic process for measuring this pressure
The static pressure is of the still fluid not yet affected by the air's speed

Pitot-Static Tubes: Static Pressure

Static pressure measurements rely on probes that face the direction of the flow, but positioned such that the flow is not accelerated through the probe
Probe shape, probe blockage, and hole position can affect the measuring results.

Pitot-Static Tubes: Wall Boundary Effects

The measurement of static pressure is sensitive to distance from solid borders.
Fluid acceleration creates a reduced static pressure in proximity of the wall
For optimal accuracy, static pressure measurements should be taken a certain minimum distance away from the wall

Pitot-Static Tubes: Dynamic Pressure

Dynamic pressure is the difference between total pressure and static pressure.
Formula for calculating dynamic pressure is used using pressure difference in the pitot-static tube.
Typically small pressure difference for air flow compared with the case for liquid flow.

Dynamic Response of Pitot-Static Tubes

The dynamic response depends on pressure passage length, manometer size, and volume displacement of the manometer; which is inversely proportional to the tube diameter, so having smaller tubes ensures faster response time

Pitot Tubes for Multi-Dimensional Flows

Pitot static probes come in several configurations (2 hole, 5 hole, 7 hole) to suit different flow scenarios

Seven-Hole Pitot-Static Tube

The device measures total, static, and the 3 velocity components.
Calculates flow angles (yaw and pitch) in the measurement process

Pressure Measurements in Flow Fields

Static pressure occurs when fluid is at rest
Dynamic pressure is induced when fluid moves
Stagnation or total pressure is the total pressure which depends both on rest fluid (static) and moving fluid (dynamic) pressure.

Bernoulli's Equation

A formula which describes the relationships between flow velocity, static pressure, and the potential energy of a fluid flow along a streamline at a constant density.

Pressure Sensitive Paints (PSP)

A paint-like coating that fluoresces in relation to air pressure.
Used for measuring local pressure in aerodynamic situations at high precision.
Provides global, easily readable data

Pressure Sensors: Selection Guides

Offers information about the criteria for selecting the appropriate pressure sensor based on the particular needs of the user.

Gravitational Pressure Sensors: Barometers

Devices measuring ambient/atmospheric air pressure (related to weather changes).
Often uses fluid column heights (mercury, in inches, or water) for measurement.

Gravitational Pressure Sensors: Manometers

Tools that gauge pressure differences and consist of a U-shaped tube with a medium inside, which reacts to pressure differences.
The typical media used is oil, or water.
Measurement with a manometer can be done by use of an inclined U-tube

Gravitational Pressure Sensors: Inclined U-Tube Manometers

The inclined portion of a manometer allows greater movement of the fluid column per unit change in pressure.
An inclined setup improves the readability of reading, increasing sensitivity in measurement.
Provides accurate reading if properly calibrated in relation to the angle of the measuring tube

Note: The organization of the study notes has been improved and the information is grouped for better understanding. Key formulae have been included as well.

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Description

Test your understanding of force measurement methods and their principles in this physics quiz. Covering SI units, Newton's laws, and flow measurement techniques, this quiz will challenge your knowledge on both theoretical and practical aspects of force. Get ready to dive deep into the concepts of weight, ultrasonic flow meters, and more!