An open vessel is in the shape of a right-circular cone of semi-vertical angle 45° with axis vertical and apex downwards. At time t = 0 the vessel is empty. Water is pumped in at a constant rate pm³s^–1 and escapes through a small hole at the vertex at a rate kym³s^–1, where k is a positive constant and y is the depth of water in the cone. Given that the volume of a circular cone is πr²h/3, where r is the radius of the base and h its vertical height, show that

Deduce that the water level reaches the value y = p/(2k) at time

Transcribed Image Text:

dy ny = p-ky dt