Question

(c) A certain spillway for a dam is 20 m wide and is designed to carry 125 m/sec at flood stage. A 1:15 model is constructed to study the flow characteristics through the spillway. Determine the required model width and flow rate. What operating time for the model corresponds to a 24-hour period in the prototype? Neglect effects due to viscosity and surface tension. (2 + 2 + 2 = 6 marks) (d) What are distorted physical models? Use an example to illustrate the type of hydraulic problems that are best investigated using such distorted models? (1 + 3 = 4 marks)

Answer 1

Ans c) Width of model can be determined using length scale,

W_m / W_p = 1 / 15

where, W_m = width of model

W_p = width of prototype

=> W_m = W_p / 15 = 20 / 15 = 1.333 m

Now, equating Froude number,

=> V_m / (g x L_m)^1/2 = V / (g x L_p)^1/2

   => V_m / V = (L_m / L_p)^1/2

  Q_m / Q_p = A_m V_m / A_p V_p = (L_m /L_p) L_m² /L_p² = L_m^5/2/ L_p^5/2 = ( $\lambda$ _t)^5/2

=> Q_m = (1/ 15)^5/2 x 125 = 0.143 m³ /s

The time can be related to velocity, since

V = L / t

=> V_m / V = L_m t_p / L_p t_m

=> t_p / t_m = V_m L_p / V_p L_m

=> t_p / t_m = (Lp / Lm)^1/2

=> t_m = t_p / (Lp / Lm)^1/2   

Putting values,

=> t_m =  24 / 15^1/2 = 6.2 hr

Ans d) A distorted physical model is a model in which a vertical length scale is different from horizontal length scale. Example - Distorted models provides flexibility in choosing horizontal scale so that large horizontal area can be modeled in existing facilities .These model allows greater water depth and require less area whereas without distortion, model water depth is very small and results of model can be affected by properties of fluid such as surface tension and friction