## What is the length?

Length can de defined as the measurement or extent of physical quantities or objects from one terminal to another terminal. Stone age humans used finger length, step length, and so on to measure the size or displacement of an object. Nowadays, depending on how precise the measurement requires to be and the object’s size is measured, we use measuring devices for measurements like rulers and steel tape. Most people have used a ruler or tape measure to measure a particular distance or the size of an object. For more precise measurements of tiny objects, the development of measurement tools such as the Vernier caliper, which permits us to measure dimensions within 1/1000 of an inch. In the last few decades, electronic distance measuring instruments (EDMI) have been implemented that permit us to measure distances from a few feet to many miles with reasonable accuracy.

## General terminologies

**Civil engineering definition:** It is the concept of construction, execution, and management of townships, buildings that require technical skills and experience and prediction of their duration.

**Length definition:** The measurement or extent of physical quantities or objects from one terminal to another terminal; the greater of the greatest of two or three-dimensional values of an object respectively.

**Length-related variable’s definition:** Any particular value in relation to length to assess its changes on a specified (XY) plane.

## Dimensional analysis of length

The base measure for length is expressed in meters ‘m’ and its dimensional formula is [L]. The distance measured in ‘meters’ is a dependent variable whereas time has always been the independent variable. In science, technology, engineering, and math (STEM) give us a method to analyze the relationship of various physical quantities and fundamental quantities. [M], [T], and [L] known as mass, time, and length respectively are fundamental dimensions and the physical quantities of the above mentioned. For example, velocity is represented as [LT^{-1}] and force as [MLT^{-2}].

## Important conversions and units for measurement

- 1 meter = 3.28 feet
- 1 kilometer = 0.621 miles
- 1 inch = 2.54 centimeter
- 1 mile = 5280 feet
- 1 yard = 3 feet
- 1 acre = 43,560 ft
^{2}= 0.00156 mi^{2}= 4047 m^{2}

## Usage of length variables

It is used in radians as a ratio of two lengths, strain as a ratio of two lengths, volume, speed and distance problems, perimeter-related problems, area-related problems, projectile problems, curve types, types of units like non-standard units and standard units, types of terrain used to measure length, independent variables, regression equations and so on. Also, length number is used in coding, for example, getting the number of digits in an integer, finding even and odd numbers, composite numbers, and so on by giving the ‘string’ command.

## Usage of time variables in civil engineering

### Basic formulae

- Area of rectangle = length x breadth
- Area of parallelogram = base x height
- Area of triangle = 0.5 x base x height
- Area of trapezoid = [(a + b)/2] h
- Surface area of a 3-D rectangle (bottom edge) = length x width

### Coordinate geometry

An ordinal variable is one where the sequence or chronology of the ordinal value matters but not the difference between the values. For instance, employees ask for feedback from clients on a 1 to 5 scale, thus if one gives 4 and the other 5, that means the other person liked the service more than the first person but the difference between the interval of 4 and 5 does not count.

An interval variable is one where the difference between two values holds importance. The temperature difference between the interval of 100 degrees and 90 degrees is equal to that of 90 degrees and 80 degrees.

### Environmental engineering

It deals with the conservation of resources by using renewable sources and researching technical ways to adopt practices for environment-friendly techniques along with cost analysis for prediction of long terms expenses and savings.

#### Storm water runoff

To calculate the peak stormwater runoff rate during heavy rainfall, the below formula is required wherein is different for different locations.

Q = C_{f} C_{i} A

Here,

Q = rate of peak storm water runoff (ft^{3}/s)

C_{f} = runoff coefficient adjustment factor

C = runoff coefficient

I = rainfall intensity (in./h)

A = drainage area (acres)

Thus, ‘A’ is the length-related variable.

#### Water supply (Hazen-Williams formula)

It is the mathematical expression for evaluation of head loss, it uses the flow of water and the properties of the pipe and is helpful for irrigation and sprinkler systems.

${h}_{f}=\frac{10.44L{Q}^{1.85}}{{C}^{1\xb785}{d}^{4\xb78655}}$

Here,

h_{f }= head loss due to friction

L = length of pipe (ft)

Q = water flow rate (gallons per minute)

C = Hazen William’s constant

d = diameter of the pipe (in.)

Thus, ‘L’ and ‘d’ are length-related variables.

### Soil mechanics

It deals with soil exploration and tests, the concept of properties of various soils and analyzing how it can be beneficial for man-made structures.

#### Constant head permeability test

It is the laboratory method used for coarse-grain soil.

$k=\frac{QL}{Ah}$

Here,

Q=Volume of water collected in time t

L=distance between manometer taping point

A=Cross sectional Area of sample

h= difference in manometric liquids

Thus, ‘L’ and ‘A’ are length-related variables.

#### Falling head permeability test

It is the laboratory method used for fine-grain soil.

$K=\frac{2.303aL}{At}{\mathrm{log}}_{10}\left(\frac{{h}_{1}}{{h}_{2}}\right)$

Here,

a = Area of tube (m^{2})

A = area of sample (m^{2})

t = time in ‘sec’

L = length in ‘m’

H1 = upstream edge level at t=0

H2 = upstream edge level after time ‘t’

Thus, ‘L’, ‘a’, and ‘A’ are the length-related variables.

### Fluid mechanics

It is the study of water or any liquid which flows freely, its behavior, characteristics, etc.

#### Continuity Equation (conservation of Mass)

When comparing any 2 substances having a linear relationship with density, area, and volume, equating both of them refers to the continuity equation.

${\rho}_{1}{A}_{1}{V}_{1}={\rho}_{2}{A}_{2}{V}_{2}$

Here,

ρ = density

A = area

V= volume

Thus, ‘A’ and ‘V’ are length-related variables.

## Context and Applications

This topic has a wide range of applications in the field of

- Bachelors of Technology in Civil Engineering
- Bachelors of Technology in Geotechnical Engineering
- Masters of Technology in Geotechnical Engineering

## Practice Problems

1. What is the dimensional formula of length?

- L
- (L)
- [L]
- L

Correct option- c

Explanation: [L] is the dimensional formula of length.

2. 1 mile is how many feet?

- 5500
- 5280
- 5000
- 5820

Correct option- b

Explanation: 1 mile = 5280 feet

3. What is ‘L’ in the constant head permeability test equation?

- Distance between manometer taping point
- Distance between manometric liquid levels
- Both a and b
- None of these

Correct option- a

Explanation: ‘L’ in the constant head permeability test equation is the distance between the manometer taping point.

4. Which of the following is correct?

- Area of parallelogram: length x base x height
- Area of parallelogram: 0.5 x base x height
- Area of parallelogram: base + height
- Area of parallelogram: base x height

Correct option- d

Explanation: Area of a parallelogram is equal to base x height.

5. What is the full form of EDMI?

- Electronic Displacement Measuring Instruments
- Electronic Distance Moving Instruments
- Electronic Distance Measuring Instruments
- None of these

Correct option- c

Explanation: The full-form of EDMI is Electronic Distance Measuring Instruments.

## Related Concepts

- Velocity
- Frequency
- The regression equation
- Distance
- Speed

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