The spout heights in the container are 10 cm, 20 cm, 30 cm, 40 cm. The water level is maintained at a ...?

Question

45 cm height by an outside supply. a) What is the speed of the water out of each hole? b) Which water stream has the greatest range relative to the base of the container? If you could show me the process of getting the answer so I understand it I'd appreciate it. Thank you

Answer 1

This is more of an engineering question (meaning an exact answer is impossible but an approximation can be made). One basic equation used for flow velocity through an orifice is (from the ref.):
V = Cv*sqrt(2gh), where h=head and Cv is a velocity coefficient that varies with the liquid, orifice type, geometry, etc. but usually is nearly 1. This equation is based on the assumption that potential energy is converted to kinetic energy, thus V^2/2 = gh. Presumably Cv embodies the many factors that can reduce velocity such as viscosity, surface tension and wall friction. For a "physics" answer, just assume Cv = 1 and solve.
The head is the difference between the liquid level and the orifice location, so in the 4 instances of this case
head = 0.45 - height = 0.05 m, 0.15 m, 0.25 m and 0.35 m.
To get the distance, use the standard gravity kinematics, i.e.:
time of fall t = sqrt(2*height/g)
distance = Vt
If you combine the equations for V, t and head, g drops out:
distance = Vt = sqrt(2g*(0.45-height)) * sqrt(2*height/g)
= 2*sqrt(0.45*height-height^2)