You are asked to design a micro hydropower system, which is simplified as the figure below....

 

Transcribed Image Text:

You are asked to design a micro hydropower system, which is simplified as the figure below. 1-ton of water at 25°C is stored in a cylindrical tank, and water is being drained through a pipe, whose inner diameter is D, horizontally placed at the bottom of the tank. It is assumed that the efficiency of the turbine is 75% and the velocity of water after the turbine is zero. H(t) duz др əz Pat AT turbine The dynamic equations for the flow through the capillary are given as follows: drain a 10 10 r. (r du ² ) = 9H (0) + µ = 0 (rou) L (1) If the flow is slow enough, quasi-steady flow assumption is applied, u₂ = - [₁-(2)]. Find the expression of the wall shear stress at the pipe wall. (2) Find the expression of H(t) as a function of time. (3) How long does it take to 99% empty the tank? (4) Find the expression of the rate of the electricity generation (J/s). (5) Find the expression of the overall electricity generation (J) until the tank is 99% empty. C(t)R² 4μ (6) To maximize the overall electricity generation (J), how the cross-sectional area of the tank Ay should be chosen? (7) If the pipe is vertically attached at the bottom of the tank, repeat the calculations from (1) to (6). You are asked to design a micro hydropower system, which is simplified as the figure below. 1-ton of water at 25°C is stored in a cylindrical tank, and water is being drained through a pipe, whose inner diameter is D, horizontally placed at the bottom of the tank. It is assumed that the efficiency of the turbine is 75% and the velocity of water after the turbine is zero. H(t) duz др əz Pat AT turbine The dynamic equations for the flow through the capillary are given as follows: drain a 10 10 r. (r du ² ) = 9H (0) + µ = 0 (rou) L (1) If the flow is slow enough, quasi-steady flow assumption is applied, u₂ = - [₁-(2)]. Find the expression of the wall shear stress at the pipe wall. (2) Find the expression of H(t) as a function of time. (3) How long does it take to 99% empty the tank? (4) Find the expression of the rate of the electricity generation (J/s). (5) Find the expression of the overall electricity generation (J) until the tank is 99% empty. C(t)R² 4μ (6) To maximize the overall electricity generation (J), how the cross-sectional area of the tank Ay should be chosen? (7) If the pipe is vertically attached at the bottom of the tank, repeat the calculations from (1) to (6).

Answer rating: 100% (QA)

ANSWER ATTACHED IMAGE Solution When the tube is kept inclined to the vertical the length of the uppe... View the full answer