Grain pours out of an inverted conical silo which comes to a point at the base. the silo top diameter is 20m and it stands 40m tall. The grain leaves via a 400mm opening at the base with a velocity V.V=(2gh)^0.43How long does it take the level to fall from the top by a distance of 26m?thank for your help
Calculus problem... i'm going to use V for Volume and v for velocity 1) figure out how much volume is flowing through the opening assuming the opening is round, d=.4m and h is constantly changing dV/dt = A*v = pi*.4^2/4*(2*g*h)^.43 (m^3/s) V(dot) = .126*(19.62*h)^.43 = .453*h^.43 (m^3/s) V(dot @ h=40) = 2.21 m^3/s V(dot @ h=14) = 1.41 m^3/s 2) Volume of a cone = pi*d^2*h/12 (www.grc.nasa /WWW/K-12/airplan... V(40m) = 104.7*40 = 4188 m^3 for at V(14m), take the ratio of diameters ==> 20/40 = d/14 therefore d(14m) = 7 m V(14m) = 179.6 m^3 Change of Volume = 4188-180 = 4008 m^3 I'm stuck, hope I could give you a start.
