Question

1. 5 meter wide retaining wall made of concrete with density of 2500kg /m3 is filled with water having density of 1000kg per metre cube on one side . determine the height of filling up to which the wall is safe against overturning when the water is filled up to maximum height of the retaining wall .The location of the retaining wall is is (770 ‘ 36mints ) east and 380 42mints east.Note that. the acceleration due to gravity changes with the latitude.

Answer 1

The variation of g is only approx. 0.5% from equator to pole and hence in engineering terms is insignificant in this case.

The question is almost incomprehensible. THe following is my interpretation of the information - but it may be that I have misunderstood:



This is a cross section of the wall - we do not know how long it is (but that doesn't matter)

I think the question means how high can the wall be so that IF it was filled to max height it would be on the point of overturning.

However - the 'centre of pressure' of water is 1/3 up from the bottom whereas the c of g of the wall is 1/2 up from bottom

SO the pressure acts below the Cof G - i.e the 'toppling force ' will cause the dam to fall backwards! ( surprise me - slightly counter intuive - but the physics seems sound to me so I'll carry on...)

So you have pressure force (per linear length) of rho gh acting at 1/3 h
You have a concrete weigh rho Ag actin through co f g

Taking moments about bottom inside corner of wall

.....
take it from there! no time to finish at the moment....