00:01
In this question we have been given that there is water which is kept at 10 degrees celsius and it is flowing steadily into a pipe from a pipe you can say and there are some other you know important quantities that has been given to us.
00:14
This question has three parts.
00:17
So let's first see how we can approach this question.
00:20
So firstly we need to calculate the reynolds number over here because we know that in such, in all these kinds of questions we need to know the actual value.
00:30
So, the basic formula for reynolds number, let's write it as re, is equal to r .e is viscosity d upon, sorry, v here is the average velocity, d is the diameter, row is the density of water, whereas everything upon mu, so mu here is the dynamic viscosity of water.
00:54
So let's substitute all the values that have been given to us.
00:58
So from here are e which is reynolds number.
01:01
So the density, we are taking the value that has been given to us in the question.
01:05
So we will not take thousand, we'll take 99 .97.
01:10
Whereas the average velocity is given to us as 0 .9 meters per second.
01:16
Whereas we've been given the diameter of this pipe to be 0 .12 centimeters.
01:24
So we can convert this into 1 .2 into 2 .2.
01:28
10 raised to the par minus 3.
01:30
So everything is converted into meters.
01:33
And mu is given to us as 1 .307 into 10 ratio to the power minus 3.
01:41
So mu here is a dynamic viscosity.
01:44
So it's already given us in the bracket.
01:46
So now, r .e, the reynolds number for this case, comes out to be 826 .07.
01:54
So this is the value.
01:55
Now we need to know that what kind of flow will it be.
02:00
So since this renault number is less than 2 ,300, so this is going to be a laminar flow.
02:08
So we calculated this renault number to actually find out what kind of flow is it.
02:14
So that we can proceed further with our question.
02:17
Now let us move on to part a of the question which is the main part.
02:22
This is where our question actually starts from.
02:25
Before this we can also calculate another important quantity which we will need in our question since it's not mentioned that it's a friction less every so we have to take friction factor into consideration so to calculate the friction factor this is equal to 64 upon the renault number this is a simple calculation so this number this value comes out to be 0 .0747 47.
02:55
So if you want you can take it up to some approximation.
02:58
Now let us actually start our first part.
03:02
So in the first part we're asked to calculate what is the pressure drop.
03:07
So we need to know the direct formula pressure drop which is del p l which is pressure you can say drop is equal to f which is a friction factor up is into l by b.
03:22
And then we have another multiplication which is row v squared upon 2.
03:28
Now let us finally put in all the values.
03:33
So this value is 0 .0747 whereas l is given to us as 15 meters the length of the pipe, whereas the diameter is given to us as 1 .2 into 10 raised up a minus 3.
03:47
Now let's move on to the second part.
03:50
So, row the density is 99 .7 into 0 .9 and this will be upon 2.
04:00
On calculation, this value, the pressure drop comes out to be approximately equal to 392 .074 kiro pascal.
04:11
So it is pressure drop.
04:13
So this is how we can calculate this specific part of our question.
04:17
Now let's move on to the next part, which is part b of the question.
04:23
So let me do it over here.
04:25
So in part b, we need to calculate what exactly is the head loss...