Homework #1
Due Data: 2025. 03. 26
1. The period of oscillation 𝑇 of a water surface wave is assumed to be a function of density 𝜌
wavelength 𝜆 depth ℎ, wave amplitude 𝐴 gravity 𝑔 and surface tension 𝜎. Rewrite this relation in
dimensionless form.
2. The drag on a sonar transducer of a sphere shape is to be predicted based on wind tunnel test data.
The prototype a 0.5 𝑚 diameter sphere is to be towed at 2.0 𝑚/𝑠 in water at 15℃ . (𝜌𝑤 =
999.0 𝑘𝑔⁄𝑚3 , 𝜇𝑤 = 1.14 × 10−3 𝑁𝑠⁄𝑚2 ).
(1) If the model is 150 𝑚𝑚 in diameter determine the required test speed in air at 25 ℃ under
dynamically similar conditions. (𝜌𝑎 = 1.19 𝑘𝑔⁄𝑚3 , 𝜇𝑎 = 1.84 × 10−5 𝑁𝑠⁄𝑚2 )
(2) If the drag of the model at these test conditions is 3.0 N estimate the drag of the prototype.
3. The drag of a 9.0 m long submarine is to be estimated from wind tunnel tests with a scale model of
length 1.6 m and wetted surface area 1.2 m2. The measured drag force in the wind tunnel is 8.5 N at a
wind speed of 32 m/s and air temperature of 25 ℃ . (oodel
𝜌𝑚 = 1.19 𝑘𝑔⁄𝑚3 𝜇𝑚 = 1.84 ×
10−5 𝑁 ∙ 𝑠⁄𝑚2)
(1) If the full-scale submarine is deeply submerged in salt water at 15 ℃ at what speed can its drag be
most accurately predicted? (Prototype
𝜌𝑓 = 1025.9 𝑘𝑔⁄𝑚3 𝜇𝑓 = 1.22 × 10−3 𝑁 ∙ 𝑠⁄𝑚2 )
(2) What is the best estimate of the drag on the full-scale submarine at a speed of 2.2 m/s?
(Note Apply the approximate relationship 𝐶𝐷 (𝑅𝑒) ≅ 𝐶𝐹 (𝑅𝑒) + 𝐶𝑃 and use the ITTC line 𝐶𝐹 =
0.075⁄(log10 𝑅𝑒 − 2 )2 for frictional drag coefficients.)
선박해양유체역학 (2025년 봄학기)