3 A tank full of liquid has a hole made in its base.
Two students, Sarah and David, propose two different models for the speed, \(v\), at which liquid exits the tank.
David thinks that \(v\) will depend on the height of the liquid in the tank, \(h\), the acceleration due to gravity, \(g\), and the density of the liquid, \(\rho\), such that \(v \propto g ^ { a } h ^ { b } \rho ^ { c }\) where \(a\), \(b\) and \(c\) are constants.
Sarah thinks that \(v\) will not depend on the density of the liquid and suggests the model \(v \propto g ^ { a } h ^ { b }\)
3
- By considering dimensions, explain which student's model should be rejected.
[0pt]
[2 marks]
3 - Find the values of the constants in order for the model that you did not reject in part (a) to be dimensionally consistent.
[0pt]
[2 marks]