(a) State and explain the principle of dimensional homogeneity. Give…

Question

(a) State and explain the principle of dimensional homogeneity. Give two examples each of dimensionally homogeneous and non-homogeneous equations. (6)

(b) A spillway design is to be studied by means of a geometrically similar model constructed to a scale of $1 : 20$. Neglecting viscous and surface tension effects, calculate :

(i) the discharge in the model corresponding to a discharge of $1500 \text{ cumecs}$ in the prototype

(ii) the velocity in the prototype corresponding to a velocity of $2 \text{ m/s}$ in the model

(iii) the height of the hydraulic jump corresponding to a jump of $5 \text{ cm}$ in the model

(iv) the energy dissipated in the prototype corresponding to $0.184 \text{ kW}$ in the model. (14)

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