Home / Questions / A cylindrical tank 5 m in diameter discharges through a mild steel pipe system
A cylindrical tank, 5 m in diameter, discharges through a mild steel pipe system (ε = 4.6 × 10^{−5} m) connected to the tank base as shown in the figure below. The drain pipe system has an equivalent length of 100 m and a diameter of 23 cm. The tank is initially filled with water to an elevation of H with respect to the reference plane.
a) Apply the Bernoulli equation, Eq. (5) in Problem 7.7, to the region between planes “1” and “2” and show that
where L_{eq} is the equivalent length of the drain pipe.
b) Consider the tank as a system and show that the application of the unsteady-state macroscopic mass balance gives
Analytical integration of Eq. (2) is possible only if the friction factor f is constant.
c) At any instant, note that the pressure drop in the drain pipe system is equal to ρg(h−H^{∗}). Use Eqs. (4.5-18)–(4.5-20) to determine f as a function of liquid height in the tank. Take H^{∗} =1 m, H = 4 m, and the final value of h as 1.5 m.
Eqs. (4.5-18)
Eqs. (4.5-20)
d) If f remains almost constant, then show that the integration of Eq. (2) yields
Calculate the time required for h to drop from 4 m to 1.5 m.
e) Plot the variations of <v_{2}> and h as a function of time on the same plot. Show that dh/dt is negligible at all times in comparison with the liquid velocity through the drain pipesystem.
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