Volume of water

[Denton91]

Water flows through a 250mm diameter drain to a depth of 80mm. Calculate a)the length of the wetted perimeter of the drain and b)the volume of water contained in a 2m long section of the drain.

i have worked out A, by working out the radians of the wetted area, then doing r X rads to get the wetted perimeter at 300.625mm. I've then gone to do B, firstly working out the volume of the cylinder, using Pi x r x r x l. I have tried many a way of trying to find an answer, but I aren't happy with any.


JUST editing to say I've just realised I've done part A wrong from re-reading the question

 

[Deleted member 4993]

Water flows through a 250mm diameter drain to a depth of 80mm. Calculate a)the length of the wetted perimeter of the drain and b)the volume of water contained in a 2m long section of the drain.

i have worked out A, by working out the radians of the wetted area, then doing r X rads to get the wetted perimeter at 300.625mm. I've then gone to do B, firstly working out the volume of the cylinder, using Pi x r x r x l. I have tried many a way of trying to find an answer, but I aren't happy with any.


JUST editing to say I've just realised I've done part A wrong from re-reading the question

cos^-1(45/125) = 1.202528

wetted circumference of cross-section = (2*1.202528) * 125 mm

Now continue.....

 

[Denton91]

cos^-1(45/125) = 1.202528

wetted circumference of cross-section = (2*1.202528) * 125 mm

Now continue.....

Thanks for your help...i must have been having a big dose of brain freeze when I originally tried this question, as it all seemed so obvious about 6 hours later whilst I was watching TV!!

 

[Denton91]

Hello again everyone.

I've been tasked with finding a secondary method to check our answers with. Obviously, i have found the answers already. To find part A (the wetted perimeter) I have found the arc length, by first sketching the circle, with the 80mm of flowing water, and sketching a triangle from there to the centre of the circle.

I worked out the height of said triangle (r-80=45mm)...

calculated the overall angle of the triangle (2*cos^-1(45/125)) to give me 137.798^o...

I then worked out the arc length by doing (137.798/360)*(2*Pi*125)=300.629



For part B (working out the volume of water contained in 2m long section of drain) I first worked out the area of the sector using info. from A...

(137.798/360)*(Pi*125²)=18789.288mm...

Then I worked out the area of the triangle (0.5*125²*sin(137.798))=5247.918...

I then I worked the segment area out (18789.288-5247.918)=13541.37...

I then multiplied that by 2 to give me an overall answer of 27082740mm³.


I have only been given today to do this, along with 4 other questions (2 of which I think I have done) and so my brains starting to hurt a little now. If anyone could even tell me even just where to find ways of alternate methods, I would be greatly appreciative.