Problem 1 (35 points
The figure below shows a water (\(\rho = 1000\) kg/m³) in a lightweight tank hanging from a network of cables.
The tank contains two inlet ports (\(D_1 = D_2 = 8\) cm) and two outlet ports (\(D_3 = D_4 = 5\) cm). Flow through
all the inlets and outlets can be turned on/off. Both inlets have the same velocity magnitude (\(V_1 = V_2\)), and
similarly, \(V_3 = V_4\). The tank weighs 35 N when empty and has an inner diameter of 60 cm.
Now consider three scenarios:
a. Inlet ports 1 and 2 are completely closed, but 3 and 4 are open with velocity magnitudes \(V_3 = V_4 =\
2.5 m/s\): calculate the rate at which the height of water in the tank is changing. Is it increasing or
decreasing?
b. Outlets 3 and 4 are completely closed but 1 and 2 remain open: estimate the tension in cable AB at
the instant when the water height in the tank is 50 cm.
c. All inlet and outlet ports are fully open with \(V_3 = V_4 = 2.5\) m/s and the water in the tank is kept at
a steady height of 50 cm: compute the tension in cable AB.
Note: in (b) and (c), neglect any unsteady effects of fluid velocity within the tank.