Question

17.16 A ship 150 m long moves in fresh water at 15°C
at 36 km/hour. A 1:100 model of this ship is to
be tested in a towing basin containing a liquid
of sp. gr. 0.90. What viscosity must this liquid
have for both Reynolds and Froude model laws
to be satisfied? At what speed must the model
be towed? If 117.7 watts is required to tow the
model at this speed, what power is required by
the ship? Dynamic viscosity of water at 15°C is
1.13 x 10-N.s/m²
[Ans. 1.017 ~ 10 N.s/m²; 1 m/s;
1.308 x 109kW]​

Answer 1

Explanation:

ship 150 m long moves in fresh water at 15°C at 36 km/h. A 1:100 model of

this ship is to be tested in a towing basin containing a liquid of specific gravity

0.90. What viscosity must this liquid have for both Reynolds and Froude model

laws to be satisfied ? At what speed must the model be towed ? If 117.7 watts is

required to tow the model at this speed, what power is required by the ship ?

Dynamic viscosity of water at 15°C is 1.13 × 10–3 N.s/m2.

Answer 2

Concept:

Froude Model law can be defined as,

u /√l = v /√L

Where u and l are the velocity and length of the model and v and L are the length and velocity of the actual ship.

Reynold's Model law can be defined as,

ul/ν₁ = vL/ν₂

Where u, l, and ν₁ are the velocity, length, and kinematic viscosity of the model respectively, and v, L, and ν₂ are the velocity, length, and kinematic viscosity of the actual ship.

Given:

Length of Ship, L = 150 m

Model of the ship and Ship ratio: 1:100

Velocity, v = 36 km/h = 10 m/s

Specific gravity, sg= 0.90

Dynamic viscosity of water at 15°C, ν₂= 1.13×10⁻³N.s/m²

Find:

The viscosity of the liquid, and the speed, and power required by the ship.

Solution:

The ratio of the Model of the ship and Ship is 1:100.

Length of model, l = 1/100 × 150 = 1.5

Calculation of viscocity,

For this, the speed must be calculated,

u /√l = v /√L

Substituting the values,

u = v √( l / L ) =  10 √ (1/100)

u = 10/10 = 1 m/s

Combining both the laws, Froude and Reynolds,

ν₁/ν₂ = ul×δ/vL

ν₁ = [ν₂ × 0.9] / (1000) = (1.13×10⁻³ ×  0.9) /1000

ν₁ = 1.017 ×10⁻⁶   N.s/m²

Power Required by ship,

P = p (Lv/lu)²/δ = (117.7)× (100 ×10)² / 0.9

P = 1.308 × 10⁸ W

Hence, the viscosity of liquid for which both Reynolds and Froude model laws will be satisfied is 1.017 ×10⁻⁶ N.s/m², the speed towed by the model is 1 m/s and if 117.7 watts is required to tow the model at this speed, the power required by the ship is 1.308 × 10⁸ W.

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