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Question 7 [15 marks] The following diagram shows a water tank: D h0 h(t) Stopper Water flow d The initial water level in the tank is h0, the water level drops continuously after the stopper is left opened. If this process of draining is continuous, i.e., ?t ? 0, the whole process can be described by the differential equation: dh/?h - ?2g (d²/D²) dt = 0, where h is the water level after time t, D is the diameter of tank, d is the diameter of outflow pipe and g is the gravity constant. a) Solve the differential equation and express the solution in terms of h. [10 marks] b) Find the constant of integration in part (a) subject to the initial condition: h(0) = h0. [5 marks]

          Question 7 [15 marks]
The following diagram shows a water tank:
D
h0
h(t)
Stopper
Water flow
d
The initial water level in the tank is h0, the water level drops continuously after the stopper is left opened. If this process of draining is continuous, i.e., ?t ? 0, the whole process can be described by the differential equation:
dh/?h - ?2g (d²/D²) dt = 0,
where h is the water level after time t, D is the diameter of tank, d is the diameter of outflow pipe and g is the gravity constant.
a) Solve the differential equation and express the solution in terms of h. [10 marks]
b) Find the constant of integration in part (a) subject to the initial condition: h(0) = h0. [5 marks]

Question 7 [15 marks]
The following diagram shows a water tank:
D
h0
h(t)
Stopper
Water flow
d
The initial water level in the tank is h0, the water level drops continuously after the stopper is left opened. If this process of draining is continuous, i.e., ?t ? 0, the whole process can be described by the differential equation:
dh/?h - ?2g (d²/D²) dt = 0,
where h is the water level after time t, D is the diameter of tank, d is the diameter of outflow pipe and g is the gravity constant.
a) Solve the differential equation and express the solution in terms of h. [10 marks]
b) Find the constant of integration in part (a) subject to the initial condition: h(0) = h0. [5 marks]

Added by Steven J.

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