Model Analysis

Q.

The S.I unit of viscosity is _________.

Q.

Water flows into a large tank with a flat bottom at the rate of ${10}^{-4}{m}^3{s}^{-1}$. Water is also leaking out of a hole of area $1c{m}^2$ at its bottom. If the height of the water in the tank remains steady, then this height is

1. $5.1cm$

2. $4cm$

3. $2.9cm$

4. $1.7cm$

Q. A river model is constructed to a horizontal scale of 1 : 1000 and a vertical scale of 1 : 100. A model discharge of 0.1 $m^3$/s would correspond to a discharge in the prototype, of what magnitude?

1. ${10}^2{m}^3/s$
2. ${10}^3{m}^3/s$
3. ${10}^4{m}^3/s$
4. ${10}^5{m}^3/s$

Q. The height of a hydraulic jump in the stilling pool of 1:25 scale model was observed to be 10 cm. The corresponding prototype height of the jump is

1. not determinable from the data given
2. 2.5 m
3. 0.5 m
4. 0.1 m

Q. The distorted models, used in the hydraulic studies, are those which

1. have exaggeration of the vertical scale and horizontal scale
2. are not geometrically similar to the prototypes
3. have same vertical and horizontal scale as that of the prototypes
4. have same Froude number as that for the prototypes

Q. In a 1/50 model of a spillway, the discharge was measured to be $0.3m^3/sec.$ The corresponding prototype discharge in $m^3/sec$ is

1. 2.0
2. 15.0
3. 106.0
4. 5303.0

Q. A river whose discharge is ${10}^5$ cumecs is to be studied by a 1 : 100 scale model in a laboratory. The discharge required in the model is:

1. 0.5 $m^3/s$
2. 10 $m^3/s$
3. 1 $m^3/s$
4. 5 $m^3/s$

Q. A model of a weir made to a horizontal scale of 1/40 and vertical scale of 1/9 discharges 1 lps. Then the discharge in the prototype is estimated as

1. 1 lps
2. 108 lps
3. 1080 lps
4. 10800 lps

Q. For homologous model of a pump built to a scale ratio of 1 : 2, fluid and speed being the same in model and prototype, the ratio of model power to prototype power is

1. 1/2.82
2. 1/4
3. 1/8
4. 1/32

Q. A 1 : 25 model of a naval ship is towed at a velocity of 1.2 m/s to determine each of the two components of the total drag that may be experienced by the prototype. The wave-making drag of the model is duly estimated to be 0.37 kgf. What would be the wave making drag on the prototype ship?

1. 1250 kgf
2. 1875 kgf
3. 5781.2 kgf
4. 4635 kgf

Q. A model of a boat is built to a scale of 1/100. It experiences a resistance of 0.10 N when simulating a speed of 5 m/s of the prototype. Water is the fluid in both the cases. Neglecting frictional forces, corresponding resistance in the prototype is:

1. 1000 kN
2. 100 kN
3. 10 kN
4. 1 kN

Q. Distorted models are needed for:
1. Rivers
2. Dams across wide rivers
3. Harbours

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

Q. A spillway of an irrigation project is to be studied by means of a model constructed to a scale of 1 : 9. The prototype discharge is 1000 $m^3/s.$ Neglecting the viscous and surface tension effects, the required flow rate for the model is

1. 12.35 $m^3/s$
2. 111.11 $m^3/s$
3. 4.11 $m^3/s$
4. 1.37 $m^3/s$

Q. In the model of a highway bridge constructed to a scale of 1:25, the force of water on the pier was measured as 5 N. What is the force (approximate) on the prototype pier?

1. 15.6 kN
2. 25.3 kN
3. 78 kN
4. 90 kN

Q. A 1 : 30 model of an ogee spillway crest records an acceleration of $1.3m/s^2$ at a certain location. The homologous value of the acceleration in the prototype in $m/s^2$, is

1. 0.043
2. 0.237
3. 1.300
4. 7.120

Q. An 1:50 model of an ogee spillway crest records an acceleration of $1.5m/se{c}^2$ at a certain location. The homologous value of acceleration in the prototype is

1. 1.5

Q. In order to estimate the energy loss in a pipeline of 1 m diameter through which kerosene of specific gravity 0.80 and dynamic viscosity 0.02 poise is to be transported at the rate of 1 $m^3/s$, model tests were conducted on a 0.1 m diameter pipe using water at ${20}^{\circ }C$ is 1.00 $\times {10}^{-2}$ Poise, then the discharge required for the model pipe would be

1. $60l/s$
2. $80l/s$
3. $120l/s$
4. $160l/s$

Q.

The magnitude of zero error of the spring balance and least count of the measuring cylinder, shown here, are respectively:

1. $2.5gand0.1mL$

2. $5gand0.1mL$

3. $2.5gand0.2mL$

4. $5gand0.2mL$

Q. The performance of a hydraulic structure during a flood has been investigated in a 1/25 model based on Froude law of similarity. A flood wave passing through the model in 2 hrs. Corresponds to a prototype period of:

1. 50 hr
2. 12.5 hr
3. 10 hr
4. 0.4 hr

Q. 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.

1. $L_r^{3/2}$
2. $L_r^{1/2}$
3. $L_r^{5/2}$
4. $L_r^{1/3}$

Q. Which one of the following statements is not correct?

1. Models are always smaller than the prototypes.
2. Dynamic similarity between a model and a prototype can be verified by equating Reynolds number in a viscous flow.
3. Match number achieves significance when the velocity of fluid approaches or exceeds the sonic velocity.
4. Distorted models are always exaggerated on a vertical scale.

Q.

State whether the following statements are true or false.

In a vernier caliper, if $1\mathrm{M}.\mathrm{S}.\mathrm{D}.=0.1\mathrm{cm}$ and the least count is $0.1\mathrm{mm}$, then $1\mathrm{V}.\mathrm{S}.\mathrm{D}.=0.9\mathrm{mm}$

1. True
2. False