In model similarity, if gravitational and inertial forces are the only important forces, then what is the discharge ratio?
Where $L_{r}$ = ratio of length dimension.

L_{r}^{3 / 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

L_{r}^{1 / 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

L_{r}^{5 / 2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

L_{r}^{1 / 3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $L_{r}^{5 / 2}$
If gravitational and inertial forces are the only important forces, then the Froude number must be the same in the model and prototype. Thus

$\frac{V_{m}}{\sqrt{g L_{m}}} = \frac{V_{p}}{\sqrt{g L_{p}}}$
But g is same for both model and prototype
$∴ \frac{V_{m}}{V_{p}} = \sqrt{\frac{L_{m}}{L_{p}}} \Rightarrow V_{r} = \sqrt{L_{r}}$
Now, Discharge= Area $\times$ Velocity
$\Rightarrow Q_{r} = A_{r} \times V_{r} \Rightarrow Q_{r} = L_{r}^{2} \times (L_{r})^{1 / 2} = L_{r}^{5 / 2}$

Suggest Corrections

Similar questions

Q. The relationship between the length scale ratio

L_{r}

and the velocity scale ratio

V_{r}

in hydraulic models, in which Froude dynamic similarity is maintained, is

Q. The flow of glycerin (kinematic viscosity

v = 5 \times 10^{- 4} m^{2} / s

) in an open channel is to be modeled in a laboratory flume using water

(v = 10^{- 6} m^{2} / s)

as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e ratio of prototype to model dimensions) for maintaining dynamic similarity?

Centripetal force is present in both inertial and non inertial frame of reference then how centrifugal force is only present in non inertial frame of reference, it simply means that it is absent in inertial frame of reference , is it true?

Q. The ________ is the ratio of inertial forces to viscous forces.

Q. Three particles, each of mass

m

, are fixed at the vertices of an equilateral triangle of side length

a

. The only forces acting on the particles are their mutual gravitational forces. Then answer the following question.
The gravitational potential at

O

Join BYJU'S Learning Program

In model similarity, if gravitational and inertial forces are the only important forces, then what is the discharge ratio? Where Lr = ratio of length dimension.

In model similarity, if gravitational and inertial forces are the only important forces, then what is the discharge ratio?
Where $L_{r}$ = ratio of length dimension.