A 1-30 scale model of a submarine is to be tested in a wind tunnel for its drag when it is operating at 15 km-h in ocean- The kinematic viscosity of air is 1-51- 10-5m2-s and for water 1-02 - 106 m2-s- What is the velocity of air in wind tunnel that should be maintained for kinematic similarity-

The Reynolds model law shall be applied in the case of fully submerged objects V_m L_mν_m=V_p L_pν_p ∴ V_m=V_p ( ν_mν_p ) ( L_pL_m ) =15×1.5 × 10^ 51.02 × 1 ...

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A 1:30 scale model of a submarine is to be tested in a wind tunnel for its drag when it is operating at 15 km/h in ocean. The kinematic viscosity of air is 1.51 $\times 10^{- 5} m^{2} / s$ and for water $1.02 \times 10^{6} m^{2} / s .$ What is the velocity of air in wind tunnel that should be maintained for kinematic similarity?

1500 m/s

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2000 m/s

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1850.5 m/s

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2500.5 m/s

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Solution

The correct option is C 1850.5 m/s
The Reynolds model law shall be applied in the case of fully submerged objects
$\frac{V_{m} L_{m}}{ν_{m}} = \frac{V_{p} L_{p}}{ν_{p}} ∴ V_{m} = V_{p} (\frac{ν_{m}}{ν_{p}}) (\frac{L_{p}}{L_{m}}) = 15 \times \frac{1.5 \times 10^{- 5}}{1.02 \times 10^{- 6}} \times 30 = 6661.6 k m / h = 1850.5 m / s$
The Reynolds model law ensures dynamic, kinematic and geometric similarities.

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A 1:30 scale model of a submarine is to be tested in a wind tunnel for its drag when it is operating at 15 km/h in ocean. The kinematic viscosity of air is 1.51×10−5m2/s and for water 1.02×106 m2/s. What is the velocity of air in wind tunnel that should be maintained for kinematic similarity?

The correct option is C 1850.5 m/sThe Reynolds model law shall be applied in the case of fully submerged objects VmLmνm=VpLpνp∴ Vm=Vp(νmνp)(LpLm)=15×1.5×10−51.02×10−6×30=6661.6 km/h=1850.5 m/s The Reynolds model law ensures dynamic, kinematic and geometric similarities.