Could anybody tell me please if there is a rule which may indicate us when to use "BROAD" and when to use "WIDE?
1st example: I know it is correct to say "broad daylight" but is it wrong to say "wide daylight"?
2nd example: "world wide" is correct, but what about, "world broad"?
3rd example: "Wide-awake" is correct, but could "broad-awake" be also correct?
Dictionaries are unable to explain this or if there is a rule. Can you help please?
Broad means a wide area, an area meaning something typically large and flat, and often but not always a surface. It can also refer to something applied to a wide area/surface-like thing. Broad also means wider as opposed to other in phrases such as the broad side of the house, etc.
Wide simply means there's a lot of distance from point A to B horizontally. It is often but not exclusively applied to things other than surfaces or flat things.
However, all the examples you provide - broad daylight, wide awake, world wide - these fall in the category of well-known phrases. Honestly, you should consider these phrases inseparable units. You can't substitute the other word in these phrases.
In a few words:
BROAD: expanse
WIDE: aperture
You are wide awake when your aperture of consciousness is fully open onto the world.
Daylight is broad daylight when the light is shed fully and directly upon the terrain, not obliquely where the terrain would be in both light and shadow. The light strikes the terrain "broadside", as it were, rather than in a glancing manner.
How wide is the doorway?
He painted the wall with a broad brush.
The dentist told me to open my mouth wide.
Your essay topic is too broad. Perhaps you can narrow it down from "Western Civilization" to something that can be presented in ten pages?
Sometimes you will see the words used interchangeably ("How wide is the brush?") but whenever there's an underlying idea of aperture, "wide" will surely work, and whenever there is the idea of an expanse, "broad" will work.
I realize that the OP has accepted the answer in the duplicate question of their own doing:
uses for the words BROAD & WIDE But this is the page where new answers can be submitted, so here's mine
ADJECTIVE
1. Of great or more than average width:
‘a wide road’
1.1 (after a measurement and in questions) from side to side:
‘how wide do you think this house is?’
1.2 Open to the full extent:
‘his eyes were wide with fear’
‘She gave him a wide grin as she opened the door to the passenger seat.’
1.3 Considerable:
‘But at this point, political analysts expect the Conservatives to fail by a wide margin.’2. Including a great variety of people or things:
‘a wide range of opinion’
2.1 Spread among a large number of people or over a large area:
‘It gained wide recognition among bloggers.’
2.2 Considering or dealing with the more general aspects of a situation, issue, etc.: ‘This debate raises wide issues of political theory concerning the proper role of the state.’(Oxford Living Dictionaries)
The list continues with the adverb, and noun meanings. But it also includes a helpful list of common phrases, to which I'll add some others
With the exception of the last two, all the phrases above are "fixed", you cannot substitute the term wide with broad. These expressions, and idioms have to be learnt by heart (memorised). There is no trick, no rule, no reason why someone could not say broad of the mark, or broad open except that no one does. Likewise nobody says in wide daylight, the correct idiom is ‘in broad daylight’. Always.
wide appeal (blue) vs. broad appeal (red)
wide attraction vs. broad attraction
wide area vs. broad area
wide brim vs broad brim
wide river vs broad river
wide road vs broad road
(adv) widely applied vs. (adv) broadly applied
wide face (blue) vs broad face (red) and the Ngram chart shows that the second collocation is more common.
wide feet vs broad feet
wide nose vs. broad nose
wide shoulders vs. broad shoulders
