1). Derive the equations for discharging a water tank. Use: H = 2 m, As = 1 m², \\
$\rho_{water}$ = 1000 kg/m³, K = 0.5 kg s?¹ m?¹/² Mass flow in = 0 and mass flow out \\
given by, \\
Mass flow out = K $z^{1/2}$. Calculate in the previous problem how long will it \\
take to discharge half a tank.\\
2). Derive the equations for charging a water tank. Use: H = 2 m, As = 1 m², \\
$\rho_{water}$ = 1000 kg/m³, K = 2000 kg hr?² Mass flow in = K t. Calculate in the \\
previous problem how long will it take to charge completely the tank.\\
3). A full tank (3 m height) discharges water from an output pipe following the \\
equation: \\
$W_{out}$ = K $z^{1/3}$. Calculate the time required to reduce the level to 1 m. \\
Data: As = 1 m², K = 0.2777 kg /(s m¹/²), $\rho_{water}$ = 1000 kg/m³