Power Engineering Third Class Part A1 - Lecture Flashcards

70 practice flashcards covering algebraic operations, trigonometry, mensuration, forces, heat, steam properties, gas laws, chemistry, and metallurgy.

How is the net displacement calculated if a man travels 5\,km East and then 5\,km West?

The net displacement is 0, as the negative direction nullifies the positive distance.

What is the result of adding unlike signs in algebraic addition?

Subtract the lesser quantity from the greater quantity and place the sign of the greater quantity in front of the answer.

What is the rule for algebraic subtraction?

Change the sign of the quantity being subtracted, then add the quantities algebraically.

What is the result of multiplying two negative quantities?

The result is a positive (+) answer.

What must be done to simplify an expression where a negative sign precedes brackets?

Remove the brackets and change the signs of all quantities within the brackets.

How are fractions simplified in the case of addition and subtraction?

They must be brought to a common denominator before the operation is completed.

In an algebraic expression, what does an index indicate?

The number of times that a quantity is to be taken as a factor in multiplication.

What is the rule for multiplying powers of similar quantities?

Add the indices, e.g., a^{3} \times a^{2} = a^{3+2} = a^{5}.

What is the rule for raising a power to a higher power?

Multiply the indices, e.g., (a^{2})^{3} = a^{6}.

How is a term transposed from one side of an equation to the other?

Transfer it to the other side and change its sign from + to - or from - to +.

What is the rule for the transposition of factors in an equation?

Carry it over to the other side and place it on the opposite side of the division line.

How do you solve an equation where the unknown quantity is a square root?

Isolate the root on one side and square both sides of the equation.

What is the mathematical definition of a logarithm?

The power to which a base number must be raised in order to equal the number in question.

What is the base for common logarithms (log)?

The base is 10.

What is the base for natural or Naperian logarithms (ln)?

The base is e, which is approximately 2.71828.

What is the relationship between natural (ln) and common (log) logarithms?

\ln(A) = 2.3026 \times \log(A)

How many degrees are in one complete rotation of a circle?

360^{\circ}

What is the definition of one radian?

The angle subtended at the center of a circle by an arc that is equal in length to the radius.

How many degrees are equivalent to 1 radian?

Approximately 57.3^{\circ} (\frac{360^{\circ}}{2\pi}).

What is the definition of an obtuse triangle?

A triangle in which one angle is greater than 90^{\circ}.

What is Pythagoras’ Theorem?

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: c^{2} = a^{2} + b^{2}.

In trigonometry, the x-axis of a unit circle represents which function?

The cosine function (\cos\theta).

What is the definition of the tangent of an angle (tan)?

The ratio between the sine and the cosine of the angle: \tan\theta = \frac{\sin\theta}{\cos\theta}.

In which quadrant are all three functions (sin, cos, tan) positive?

The 1st Quadrant (0^{\circ} to 90^{\circ}).

State the Sine Rule for oblique triangles.

\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}

State the Cosine Rule to find side ‘a’ in an oblique triangle.

a^{2} = b^{2} + c^{2} - 2bc\cos(A)

How many millimeters are in one meter?

1000\,mm

What is Heron's Formula for the area of a triangle given its sides?

A = \sqrt{s(s-a)(s-b)(s-c)} where s = \frac{a+b+c}{2}.

What is the formula for the area of a trapezoid?

A = \frac{a+b}{2} \times h where a and b are lengths of parallel sides.

What is the formula for the area of a circle in terms of its diameter?

A = 0.7854D^{2}

What is the formula for the volume of a sphere?

V = \frac{4}{3}\pi r^{3}

What is a vector quantity?

A quantity that has both magnitude and direction.

What is an equilibrant?

A single force that, when applied to a system of forces, will bring the system into equilibrium (equal and opposite to the resultant).

What is the difference between static and sliding friction?

Static friction resists initial movement from rest; sliding friction resists continued motion.

What is the coefficient of friction formula?

\mu = \frac{F{F}}{R{N}} where F{F} is frictional force and R{N} is normal reaction force.

What is the definition of work?

A force applied to a body over a distance, causing movement (W = F \times d).

What is the unit of power, and how is it defined?

The Watt (W), defined as 1\,J/s.

How is mechanical efficiency calculated?

\text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100

What is the formula for kinetic energy?

E_{k} = \frac{1}{2}mv^{2}

What is linear acceleration?

The rate of change of velocity: a = \frac{v-u}{t}.

What is angular velocity ($\omega$)?

The rate of angular displacement, measured in radians per second (rad/s).

Define stress in a material.

Internal resistance to an external force: \text{Stress} = \frac{\text{Load}}{\text{Area}}, measured in Pascals (Pa).

What is Young’s Modulus of Elasticity (E)?

The ratio of stress to strain within the elastic limit of a material.

What characterizes a cantilever beam?

It has one end fixed and the other end free.

What is the neutral axis of a beam?

The point in a bending beam where there is zero tension and zero compression stress.

What is the definition of mass density ($\rho$)?

\rho = \frac{\text{Mass}}{\text{Volume}}, typically expressed in kg/m^{3}.

What is relative density (specific gravity)?

The ratio of the density of a substance to the density of water (1000\,kg/m^{3}).

State the Equation of Continuity for fluid flow in a pipe.

Q = A{1}v{1} = A{2}v{2}

What is sensible heat?

Heat that changes the temperature of a substance without changing its state.

What is latent heat of fusion?

The heat required to change a unit mass of solid to liquid with no change in temperature.

What is the specific heat of water?

4.183\,kJ/kgK

What is the dryness fraction (q) of steam?

The fraction of saturated steam that is dry vapor.

What happens at the critical point of steam?

At 374.136^{\circ}C and 22090\,kPa, the latent heat of evaporation is zero and densities of liquid and vapor are equal.

State Boyle’s Law.

At constant temperature, the absolute pressure of a gas varies inversely with its volume (P{1}V{1} = P{2}V{2}).

What is an adiabatic process?

A process (compression or expansion) where no heat is transferred to or from the gas.

What is the characteristic gas constant (R) for air?

0.287\,kJ/kgK

What are valence electrons?

Electrons in the outermost shell of an atom that are involved in chemical reactions.

Describe an ionic bond.

A bond formed by the transfer of electrons from a metal atom to a non-metal atom.

What is the difference between a mixture and a compound?

In a mixture, components retain individual properties; in a compound, elements chemically bond to form a new substance.

Define a base according to Arrhenius Theory.

A substance that yields hydroxide ions (OH^{-}) when dissolved in water.

What is the pH of a neutral solution?

7

What is organic chemistry?

The study of compounds containing carbon.

What is an isomer?

Compounds with the same molecular formula but different structural arrangements.

What are the two common hardness tests for metals?

Brinell and Rockwell tests.

What property of iron is improved by the cupola process?

It converts pig iron into cast iron by adjusting carbon content and removing impurities.

What is the effect of adding nickel to steel?

It improves toughness, corrosion resistance, and helps prevent brittleness at low temperatures.

What is the purpose of a Process Flow Diagram (PFD)?

To show major equipment and process flow streams to understand general plant flow and control strategy.

What does P&ID stand for?

Piping and Instrumentation Diagram.

How does cathodic protection stop corrosion?

It forces the protected metal to act as a cathode by connecting it to a sacrificial anode or an impressed current source.

What is the purpose of ultrasonic inspection?

A non-destructive method using high-frequency sound waves to detect metal thickness and internal flaws.