ISRO Scientist Civil flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Euler method error order

The forward Euler method has local truncation error of order h squared and global error of order h. Halving the step size roughly halves the accumulated error, so it is only first-order accurate.

Newton-Raphson convergence order

Near a simple root, Newton-Raphson converges quadratically, roughly doubling correct digits each iteration. It fails when the derivative is zero or the initial guess is far from the root.

Simpson's rule requirement

Simpson's one-third rule integrates a function using parabolic arcs and requires an even number of subintervals. Its error is proportional to h to the fourth power times the fourth derivative.

Diagonal dominance convergence

A strictly diagonally dominant coefficient matrix guarantees convergence of both Jacobi and Gauss-Seidel iterations. Gauss-Seidel normally converges about twice as fast because it uses updated values immediately.

Flexure formula

The bending stress at a distance y from the neutral axis is sigma equals M y divided by I. Maximum stress occurs at the extreme fibre, and the section modulus Z equals I divided by y-max.

Euler buckling effective lengths

The Euler load is pi squared E I divided by effective length squared. Effective length factors are 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned and 2.0 cantilever.

Limiting neutral axis depth

For a singly reinforced section at the limit state of collapse, xu-lim divided by d is 0.53 for Fe 415 steel and 0.48 for Fe 500 steel, controlling the balanced section.

Slope-deflection equation

The slope-deflection equation expresses end moments in terms of chord rotation, joint rotations and fixed-end moments, using 2EI/L factors. Clockwise moments on member ends are taken positive.

Terzaghi bearing capacity equation

Ultimate bearing capacity for a strip footing equals c Nc plus q Nq plus 0.5 gamma B N-gamma. N factors depend only on the friction angle; square and circular footings use reduced gamma terms.

Coefficient of consolidation

Cv equals T times H squared divided by t, where H is the drainage path. Time factors are 0.197 for 50 percent and 0.848 for 90 percent consolidation.

Relative density of sand

Relative density compares the natural void ratio with the loosest and densest states. Values above 70 percent indicate dense sand with higher friction angle and lower settlement.

Effective stress principle

Effective stress equals total stress minus pore water pressure. Only effective stress controls shear strength, compressibility and bearing capacity; neutral stress does not mobilise friction.

Darcy-Weisbach head loss

Friction head loss in a pipe equals f L V squared divided by 2 g D. For laminar flow the friction factor equals 64 divided by Reynolds number.

Critical depth rectangular channel

Critical depth equals the cube root of q squared divided by g, where q is discharge per unit width. Specific energy is minimum at critical depth and the Froude number equals one.

Hydraulic jump sequent depth

The ratio of sequent depths equals half of the square root of one plus eight times the upstream Froude number squared, minus one. Energy loss grows rapidly with Froude number.

Duty and delta relation

Delta in metres equals 8.64 times the base period in days divided by duty in hectares per cumec. Delta is the depth of irrigation water applied over the base period.

Surface overflow rate

The surface overflow rate equals flow divided by tank plan area. In an ideal settling basin, particles with settling velocity greater than or equal to this rate are completely removed.

Breakpoint chlorination

Chlorine first oxidises ammonia and organics, producing combined chlorine with little disinfection power. Beyond the breakpoint, free residual chlorine appears and provides effective disinfection.

BOD dilution formula

Five-day BOD equals the difference between initial and final dissolved oxygen, multiplied by dilution factor and adjusted for seeded dilution water. The test runs at 20 degrees Celsius for five days.

Stopping sight distance

Stopping sight distance equals the lag distance v times reaction time plus the braking distance v squared divided by 2 g times friction plus or minus gradient.

Superelevation equation

Superelevation plus lateral friction equals design speed squared divided by 127 times radius. Maximum superelevation is 7 percent on plain terrain and 10 percent on hilly roads.

Greenshields traffic model

Greenshields assumes speed falls linearly with density. Capacity occurs at half the jam density, giving flow equal to one quarter of free-flow speed times jam density.

Webster optimum cycle length

Optimum cycle length equals 1.5 times total lost time plus 5, divided by one minus the sum of critical flow ratios. It minimises average delay at a signalised intersection.

Bowditch traverse adjustment

The Bowditch rule distributes closing error in latitude and departure in proportion to the length of each traverse leg. It suits compass and theodolite traverses of comparable precision.

NDVI formula

The Normalised Difference Vegetation Index equals near infrared minus red, divided by near infrared plus red. Values near plus one indicate dense healthy vegetation; water gives negative values.

GPS satellite requirement

At least four satellites are needed to determine three position coordinates plus the receiver clock bias. More satellites improve accuracy through redundancy and better geometry.

Target mean strength

Concrete mix design targets a mean strength of characteristic strength plus 1.65 times the standard deviation. This ensures no more than 5 percent of test results fall below the characteristic value.

PERT expected time

The PERT expected time equals optimistic plus four times most likely plus pessimistic, all divided by six. Variance equals the pessimistic minus optimistic difference divided by six, squared.

Total float in CPM

Total float equals latest finish minus earliest finish, or latest start minus earliest start. Activities on the critical path have zero total float and govern project duration.

Earned value cost index

The cost performance index equals earned value divided by actual cost. A value below one indicates cost overrun; the schedule performance index compares earned value with planned value.

Successive percentage change

Two successive changes of a percent and b percent give a net change of a plus b plus ab divided by 100. A rise and fall of the same percentage always produces a net decrease.

Average speed equal distances

When equal distances are covered at speeds v1 and v2, average speed is twice the product divided by the sum. This harmonic mean is always less than the arithmetic mean.