# Category Archives: Engineering

## Calculate the maximum achievable bridge out-of-balance voltage for an applied torque T of 103 N m given the following

Four strain gauges, with specification given below, are available to measure the torque on a cylindrical shaft 4 cm in diameter connecting a motor and load.

(a) Draw clearly labelled diagrams showing:

(i) the arrangement of the gauges on the shaft;

(ii) the arrangement of the gauges in the bridge circuit, for optimum accuracy and sensitivity.

(b) Calculate the maximum achievable bridge out-of-balance voltage for an applied torque T of 103 N m given the following:

Tensile and compressive strains  is the shear modulus of the shaft material and a is the radius of the shaft in metres.

## Find the gain and phase characteristics of the maintaining amplifier.

A solid-state capacitive humidity sensor has a capacitance given by:

C = 1.7 RH + 365pF

where RH is the percentage relative humidity. The sensor has an associated parallel resistance of 100 kΩ. The sensor is incorporated into a feedback oscillator system with a pure inductance and a maintaining amplifier. The oscillator is to give a sinusoidal output voltage at the natural frequency of the L–C circuit for a relative humidity between 5 and 100%.

(a) Draw a diagram of a suitable oscillator system.

(b) If the frequency of the output signal is to be 100 kHz at RH = 100%, calculate the required inductance.

(c) Find the gain and phase characteristics of the maintaining amplifier.

## calculate the mean velocity of the gas at maximum flow rate

A pitot tube is used to measure the mean velocity of high pressure gas in a 0.15 m diameter pipe. At maximum flow rate the mean pitot differential pressure is 250 Pa. Use the data given below to:

(a) calculate the mean velocity of the gas at maximum flow rate;

(b) estimate the maximum mass flow rate;

(c) estimate the Reynolds number at maximum flow;

(d) explain why an orifice plate would be suitable to measure the mass flow rate of the gas. (e) Given that a differential pressure transmitter of range 0 to 3 × 104 Pa is available, estimate the required diameter of the orifice plate hole (assume coefficient of discharge = 0.6, expansibility factor and velocity of approach factor = 1.0).

## Calculate an accurate value for the differential pressure developed across the chosen Venturi, at maximum flow rate.

A Venturi is to be used to measure the flow rate of water in a pipe of diameter D = 0.20 m. The maximum flow rate of water is 1.5 × 103 m3 h−1, density is 103 kg m−3, and viscosity is 10−3 Pa s. Venturis with throat diameters of 0.10 m, 0.14 m and 0.18 m are available from the manufacturer.

(a) Choose the most suitable Venturi for the application, assuming a differential pressure at maximum flow of approximately 3 × 105 Pa.

(b) Calculate an accurate value for the differential pressure developed across the chosen Venturi, at maximum flow rate. (Use the following formula for the coefficient of discharge:

where

d = Venturi throat diameter, and ReD = Reynolds number referred to pipe diameter.)

## sketch the form of the output signal when T = 2000 K.

A thermocouple has an e.m.f. of 5 mV when the hot junction is at 100 °C and the cold junction is at 0 °C. A thermopile consisting of 25 such thermocouples in series is used as a detector in a chopped, broadband pyrometer. When unchopped the power in the beam of radiation incident on the hot junction of the thermopile is given by 7.5T 4 pW, where T K is the temperature of the distant target. The beam is chopped by a semicircular disc rotating at 6000 r.p.m. The reference junction of the thermopile is at the temperature of the pyrometer

enclosure. Assuming the thermocouples are linear and the detector data given below, sketch the form of the output signal when T = 2000 K.

## calculate the power incident on the detector and the detector output current.

An optical fibre transmission system consists of a circular LED source, a 2-metre length of optical fibre and a circular PIN diode detector. Both the source and detector are positioned 100 µm from the ends of the fibre. Detailed data for the source, a glass fibre, a polymer fibre and the detector are given below. Use this data to perform the following calculations.

(a) The total power Ps emitted by the source in all directions (use eqn [15.23b]).

(b) The numerical aperture and maximum angle of acceptance of the glass fibre.

(c) The numerical aperture and maximum angle of acceptance of the polymer fibre.

(d) The source and detector are linked by the glass fibre; calculate the power input to the fibre, the fibre transmission factor, and power….

## Calculate the series and parallel resonant frequencies of the crystal.

A piezoelectric crystal has an effective mass of 10−2 kg, stiffness of 1010 N m−1 and damping constant 200 Ns m−1 . The electrical capacitance of the crystal is 1000 pF and the charge sensitivity is 2 × 10−10 C N−1 .

(a) Calculate the series and parallel resonant frequencies of the crystal.

(b) Calculate the magnitude and phase of the overall electrical impedance of the crystal at the above frequencies.

(c) The crystal is incorporated into a closed-loop oscillator system which is to oscillate at the crystal series resonant frequency. Calculate the required gain and phase of the maintaining amplifier at this frequency.

## Calculate the ‘round trip’ time TT and the fraction of received power to transmitted power.

An open steel vessel contains liquid metal to a depth of about 0.75 m. It is proposed to measure the depth of liquid using ultrasonic pulse reflection techniques. A quartz crystal attached to the base of the vessel is to act alternatively as a transmitter and receiver. Using the data given below and in

(a) Calculate the ‘round trip’ time TT and the fraction of received power to transmitted power.

(b) Choose suitable values for pulse width and repetition times.

Data

Velocity of sound in liquid metal = 1.5 × 103 m s−1

Density of liquid metal = 5 × 103 kg m−3

Power attenuation coefficient = 0.1 m−1

Natural frequency of quartz crystal = 1 MHz

## Find the difference between the frequencies of the transmitted and received beams when the flow rate is 1.13 × 103 m3 h−1.

An ultrasonic Doppler flowmeter is to be used to measure the volume flow rate of a slurry in a steel pipe of diameter 0.2 m. Two piezoelectric crystals, each having a natural frequency of 1 MHz, are positioned, a few millimetres apart, on the outside of the pipe to form an ultrasonic transmission link. The transmitting crystal directs an ultrasonic beam into the pipe so that the beam is moving in an opposite direction to the flowstream. The angle between the ultrasonic beam and the direction of flow is 60°. On average 10% of the ultrasonic power reaching each solid particle is scattered back in the direction of the receiving crystal. Assume that the slurry has the same density and sound velocity as water and a power attenuation….

## Explain in detail what modifications should be made to the transducer so that the signal entering the tissue is a close approximation to a single pulse.

An ultrasonic transmitter is in the form of a piezoelectric disc of diameter 2.5 cm and thickness 1.0 cm. The front face of the disc is placed directly onto biological tissue; the rear face is in contact with air. A pulse launched from the centre of the disc divides into two equal pulses, each of power 1 W and width 0.5 µs, one travelling towards the front face and one towards the rear face.

(a) Use the data given below to derive the form of the signal entering the tissue.

(b) Explain in detail what modifications should be made to the transducer so that the signal entering the tissue is a close approximation to a single pulse.