Formulas, Conversions and Data required to solve gate problems

Conversions

1litre= .001 cubic meter
1m^3=1000litres
1BTU(british thermal unit) = 1055 joules
1 btu/hr=3.412 joules/s
Area 
100 cents = 1 Acre
1 Acre = 4840 sq yards
1 yard = 3' or 36"
1 cents = 435.60 sq ft
1 sq. m = 10.76 sq. ft

1 Acre= 4047 sq m
2,47 cents = 1 are(100 sq meter)
2.47 acres = 1 hectare(10,000 sq meters)


Fibonacci series

Fn= Fn-1 + Fn-2
0,1,1,2,3,5,8,13,21....

Golden Ratio

 \frac{a+b}{a} = \frac{a}{b} \ \stackrel{\text{def}}{=}\ \varphi,
\varphi = \frac{1+\sqrt{5}}{2} = 1.6180339887\ldots.

Contour interval: 
The difference in altitude represented by the space between two contour lines on a map .

Scale of Aerial Photograph = Focal length/ Altitude above Ground level
Forecasting Population

Arithmatic method

dP/dt = Ka
P = P1 + Ka (t - t1)  
            P = population
            t = time

            Ka = arithmetic growth constant

Geometric method

dP/dt= KgP
lnP = lnP1 + Kg (t - t1)
Kg =lnP2-lnP1/t2-t1  = ln[P2/P1]/t2-t1
            P = population
            t = time
            Kg = geometric growth constant
            Note: lim (1+K)1/K = e = 2.718… base of the natural logarithms

                        K®0
1 lux = 1 lumen/sq meter
lux is the unit of illuminance
 Flux= illumination required(lux) x surface area(sq m)
Flux(lumen output)(received)= MF(maintenance factor) x UF(utilization factor) x Flux(installed)
depreciation factor = reciprocal of maintenance factor
lux=candela/d^2
cd(candela) = lm(lumen) / ( 2π(1 - cos(º/2)) )
for isotrophic light source(all directions), lumen = candela x 4x22/7


Room Index(RI)= Lx W/[Hm x (L+W)]
Hm=mounting height

Spacing to height ratio SHR=  1/Hm x[ (A/N)^ 1/2]

Acoustics

T(reverbaration time in seconds)=  .161x V(volume in m3)/A(sound absorption power in m2-sabine = area x coeffcient of absorption)
Lp = 20 log 10(Prms/Pref) dB
Lp2 = Lp1 + 20 log10(r1/r2)
lp-sound pressure
sound level- 10 log 10(Prms/Pref) dB

The handling capacity(lifts) is calculated by the
formula: H= 3OOxQx100 /TXP
where
H = handling capacity as the percentage of the peak population handled during 5 min period,
Q = average number of passengers carried in a car,
T = waiting interval, and
P = total population to be handled during peak morning period. (It is related to the area served by a particular bank of lifts.)

The value of ‘Q’ depends on the dimensions of the car. It may be noted that the car is not loaded always to its maximum capacity during each trip and, therefore, for calculating ‘H” the value of ‘Q’ is taken as 80 percent of the maximum carrying capacity of the car.

The waiting interval is calculated by the formula:
 T= RTT/N
iv
where
T = waiting interval;
N = number of lifts, and
RTT= round trip time, that is, the average time required by each lift in taking one full load of passengers from ground floor, discharging them in various upper floors and coming back to ground floor for taking fresh passengers for the next trip.

 

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