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A series of experiments was conducted for a ship model of 3-ft length in a water tank. The relevant variables are the length of the model, L, water density, p, tawing velocity, V, the viscosity, μ, and the gravitational acceleration, g. The experimental result was

A series of experiments was conducted for a ship model of 3-ft length in a water tank. The relevant variables are the length of the model, L, water density, p, tawing velocity, V, the viscosity, μ, and the gravitational acceleration, g. The experimental result was

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.8P
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1. A series of experiments was conducted for a ship model of 3-ft length in a water tank. The relevant variables are the length of the model, L, water density, p, tawing velocity, V, the viscosity, µ, and the gravitational acceleration, g. The experimental result was V (ft/s) 10 20 D (lbf) 0.022 0.079 50 30 40 0.169 0.281 0.45 = 60 0.618 70 0.731 The full-size ship is 150 ft long and designed to cruise at 15 knots and 20 knots in a freshwater lake (1 knot = 1.68781 ft/s). a. How many dimensionless groups can be obtained? Why? b. Use dimensional analysis to prove that the functional relationship of the drag force D=f(p, V, L, g, µ) can be simplified to Cd=f(Fr, Re), where D V Ca -, Fr= PVL Re= √gL μl PV²12 c. If the drag coefficient and Fr number are conserved, estimate the drag force for the full-size ship at the two cruising velocities. d. If the drag coefficient and Re number are conserved, estimate the drag force for the full-size ship at the two cruising velocities.
Transcribed Image Text:1. A series of experiments was conducted for a ship model of 3-ft length in a water tank. The relevant variables are the length of the model, L, water density, p, tawing velocity, V, the viscosity, µ, and the gravitational acceleration, g. The experimental result was V (ft/s) 10 20 D (lbf) 0.022 0.079 50 30 40 0.169 0.281 0.45 = 60 0.618 70 0.731 The full-size ship is 150 ft long and designed to cruise at 15 knots and 20 knots in a freshwater lake (1 knot = 1.68781 ft/s). a. How many dimensionless groups can be obtained? Why? b. Use dimensional analysis to prove that the functional relationship of the drag force D=f(p, V, L, g, µ) can be simplified to Cd=f(Fr, Re), where D V Ca -, Fr= PVL Re= √gL μl PV²12 c. If the drag coefficient and Fr number are conserved, estimate the drag force for the full-size ship at the two cruising velocities. d. If the drag coefficient and Re number are conserved, estimate the drag force for the full-size ship at the two cruising velocities.
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