Curved Surfaces Example

(View from short end of the bath)                                                (View from above)

Andy's having a bath with  his favourite duck called Tony. The bath has curved sides and is filled to the top with water; it has a height of 0.8m and is 1.5m in length. The sides of the bath have a curve of radius 0.4m.

a) What is the force exerted on one side of the bath along the curved edge?

Solution:

Vertical Force-

W1= Vρg = (0.4 x 0.4 x 1.5) x 1000 x 9.81 = 2354 N

W2=> 

Volume = 1/4πr2l = 1/4 x π x 0.42 x 1.5 = 3/50 π

Weight = Vρg = (3/50 x π) x 1000 x 9.81 = 1849 N

Vertical force= Total weight = 2354 + 1849 = 4203 N

Horizontal force- 

Fh = Fx = PA = ρghA = 1000 x 9.81 x 0.6 x (0.4 x 1.5) = 3531.6 N

Total resultant force-

FR = √((FH)2 + (FV)2) = √((3531.6)2 + (4203)2) = 5490 N

b) Using your answer from the previous question, what angle is the force exerted at?

Solution:

tan(a) = Fv/FH

a = tan-1(4203/3531.6) = 50o