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Explain different types of similarities that must exist between prototype nad model.

Mumbai University > Civil Engineering > Sem 5 > Applied Hydraulics 1

Marks: 10M

Year: May 2015

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Three types of similarities must exists between the model and prototype. They are

1) Geometric similarity 2) Kinemetic similarity 3) Dynamic similarity

Geometric Similarity:

The geometric similarity is said to exist between the model and the prototype. The ratio of all corresponding linear dimension in the model and prototype are equal.

For geometric similarity between model and prototype we must have the relation.

$\frac{L_P}{L_m} = \frac{b_P}{b_m} = \frac{D_p}{D_m} = L_r$

$L_m$ = length of model $\hspace{2cm}$ $L_p$ = length of prototype

$b_m$ = Breadth of model $\hspace{1.8cm}$ $b_p$ = breadth of prototype

$D_m$ = Diameter of model $\hspace{1.5cm}$ $D_p$ = Diameter of prototype

$L_r$ = scale ratio

For area's ratio and volume's ratio the relation should be given below:-

Area ratio $\frac{A_P}{A_m} = \frac{L_P \times b_P}{L_m \times b_m} = L_x \times L_r = L_r^2$

Volume ratio $\frac{forall_P}{\forall_m} = (\frac{L_P}{L_m})^3 = (\frac{b_P}{b_m})^3 = (\frac{D_P}{D_m})^3$

Kinematic Similarity:

Kinematic similarity means the similar of motion between model and prototype. Thus kinematic similarity is said to exist between the model and the prototype if the ratios of the velocity and acceleration at the corresponding points in in the prototype are the same. Since velocity and acceleration are vector quantities; hence not only the ratio of magnitude of velocity and acceleration at the corresponding points in the model and prototype also should be parallel.

For kinematic similarity, we must have

$\frac{V_{p1}}{V_{m1}} = \frac{V_{p2}}{V_{m2}}=V_r (velocity ratio)$

For acceleration

$\frac{ap_1}{am_1} = \frac{ap_2}{am_2} = a_r$

Dynamic similarity:-

Dynamic similarity means the similar of forces between the model and prototype. Thus dynamic similarity is said to exist between the model and the prototype if the ratios of the corresponding forces acting at the corresponding points are equal. Also the directions of the corresponding forces at the corresponding points should be same.

For dynamic similarity we have

$\frac{(Fi)_p}{(Fi)_m} = \frac{(Fv)_p}{(Fv)_m} = \frac{(Fg)_P}{(Fg)_m} = F_r [Force ratio]$