Measuring the Length

Length: Most commonly the longest dimension of a shape or object. In the International Standard of Units (SI), the standard unit of measuring the length is "Meter". It is the distance between two lines on a bar made of Platinum-Iridium alloy (90% Platinum & 10% Iridium) measured at melting point of ice, located at International Bureau of Weights and Measures, Paris.

Following are the different units of measurement and their equivalent values in meters.

Unit	Symbol	Value in Meters	Examples
Chemistry
Angstrom	Ao	0.000 000 000 1	Diameter of Proton = 10-5 Ao Diameter of Electron = 10-8 Ao Wavelength of Violet Rays = 4 000 Ao Wavelength of Red Rays = 7 000 Ao
International Standard Units – SI Units
Nanometer	nm	0.000 000 001	Generalized Use
Micrometer	micron	0.000 001
Millimeter	mm	0.001
Centimeter	cm	0.01
Kilometer	Km	1 000
Imperial Units – American Units
Point	pt	0.000 35	Length of Football pitch = 120 yd Length of Cricket pitch = 22 yd Average walk in an hour = 1 league
Inch	in / “	0.025 4
Hand	hand	0.101 6
Foot	ft / ‘	0.304 8
Yard	yd	0.914 4
Mile	mi	1 609.344
League	league	4 828.032
Marine Units
Fathom	ftm	1.828 8	Fathoms – Depth of sea at shores Nautical Mile – Navigation, Polar Exploration
Cable	cable	182.88
Nautical Mile	nmi	1 850.745 6
Horse Race Units
Horse Length	horse length	2.438 4	Horse length – Distance between horses in races
Furlong	fur	201.168 0
Land Survey Units
Link	li	0.201 2	Surveyor’s Use
Rod	rd	5.029 2
Chain	Ch	20.116 8
Astronomical Units
Earth Radius	RE	6 370 000	Distance from Earth to 1st nearest star (Sun) = 1 AU 2nd nearest star (Proxima Centauri) = 4.225 ly Center of Milky Way Galaxy = 8 000 pc Center of Andromeda Galaxy (M31) = 800 000 pc
Astronomical Unit	AU	150 000 000 000
Light-year	ly	9 460 000 000 000 000
Parsec	pc	30 840 000 000 000 000

Generalized Illustrative Example on Concrete Mix Design

The Design for Concrete Mix of Grade M20

Input

Characteristic Compressive Strength f_ck                 20 N/mm²

Maximum Aggregate Size                                       20 mm

Specific Gravity of Cement                                     3.15        (Lab Test Data)

Specific Gravity of Coarse Aggregate                     2.60        (Lab Test Data)

Specific Gravity of Fine Aggregate                          2.60        (Lab Test Data)

Calculation Part

Target Mean Compressive Strength f_ck’ = f_ck + t.s, Where

“t” is a statistic, generally taken as 1.65, where not more than 5% (1 in 20) results are expected to fall. That means, if 20 tests were conducted, only 1 test is expected to show low result.

“s” is standard deviation, depends on the expected degree of quality. In general, for “Good” degree of quality, the value of “s” is as shown in Table 1.

Grade	M10	M15	M20	M25	M30	M35	M40	M45	M50	M55	M60
fck	10	15	20	25	30	35	40	45	50	55	60
t	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65	1.65
s	2.3	3.5	4.6	5.3	6.0	6.3	6.6	7.0	7.4	7.7	7.8
fck’	13.80	20.78	27.59	33.75	39.90	45.40	50.89	56.55	62.21	67.71	72.87
w/c	0.65	0.60	0.50	0.45	0.35	0.30	0.30	0.30	0.30	0.30	0.30

Table 1: Tabular representation of Standard Deviation, Target Mean Compressive Strength and Water-Cement ratio for different grades of concrete.

Therefore, f_ck’ = 27.59 N/mm², and using this, the water-cement ratio (w/c) is determined using the graphical relation which can be approximately tabulated as shown in Table 1.

Therefore, w/c = 0.50.

From Table 2, for 20mm nominal maximum size of aggregate, entrapped air = 2%, water content = 186 kg and fine aggregate (sand) content = 35% for M20 grade concrete.

Nominal Size of Aggregate	Entrapped Air	M10, M15, M20, M25, M30, M35		M40, M45, M50, M55, M60
		Water Content	Fine Aggregate	Water Content	Fine Aggregate
10 mm	3%	208 kg	40%	200 kg	28%
20 mm	2%	186 kg	35%	180 kg	25%
40 mm	1%	165 kg	30%	-	-

Table 2: Tabular representation of Entrapped air, Water content and Fine aggregate for different nominal maximum size of aggregates and for different grades of concrete. The entrapped air and water content are for one cubic meter of concrete whereas fine aggregate is percentage of total aggregate content.

w/c ratio = 0.50 and water content = 186 kg, therefore cement content = 372 kg.

The calculation of fine and coarse aggregate content is done by using the following formulae

Where

V             absolute volume of concrete (gross volume minus entrapped air) = 1 – 0.02 = 0.98 cum

Ww        weight of water = 186 kg

Sw          specific gravity of water = 1

Wc          weight of cement = 372 kg

Sc            specific gravity of cement = 3.15

Pfa         percentage of fine aggregate = 35%

Wfa        weight of fine aggregate

Sfa          specific gravity of fine aggregate = 2.60

Wca       weight of course aggregate

Sca         specific gravity of coarse aggregate = 2.60

Implies, Wfa = 615 kg and Wca = 1,142 kg

Therefore, the mix becomes

Water                                   = 186 kg

Cement                                 = 372 kg

Fine Aggregate (Sand)           = 615 kg

Coarse Aggregate                  = 1,142 kg

If cement is considered as 1 part, then sand is 1.65 parts and Coarse aggregate is 3.07 parts, hence, the proportion is 1 : 1.65 : 3.07.

Note: This is the most generalized procedure for designing a concrete mix. However, for accurate proportions, factors such as: gradation, water absorption, surface moisture of fine and coarse aggregates, compaction factor etc., should be taken into account.