A vertical dam retains 18m of water It is pierced at the bas

A vertical dam retains 18m of water. It is pierced at the base by a rectangular door 4m wide and 5m high, as indicated in the figure above.

ii) In Newtons, what is the total hydrostatic force exerted on the door? Give the answer correct to 3 significnt digits

force on door= pressure on door *area of door

area of door =4*5=20m^2

pressure on door varies with depth .

pressure = p g h where p is density=1000, 9=9.8, h is height from surface of water. h=18-y

froce=20*average pressure=20*(1/(5-0)) integral[5 to 0]p*g* (18-y)dy =(20/5) integral[5 to 0]9800(18-y)dy

force=(20*9800/5)*(18y- y^2 /2)from(5 to 0)

=(20*9800/5)*(18*5- 5^2 /2 -0)

=20*9800*(18 -5/2)

=20*9800*(18-2.5)

=20*9800*15.5

=3038000