A survey launch with waterline length m travels steadily at m s through deep seawater…

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves, acoustics and compressible flow

Fluids and Continuum Physics, Ch Acoustics: sound propagation, radiation and attenuation

Problem

A survey launch with waterline length

L = 9.0

m travels steadily at

U = 11

m s

^{-1}

through deep seawater of density

\rho_0 = 1025

kg m

^{-3}

and adiabatic bulk modulus

K_s = 2.34\times10^{9}

Pa. Take

g = 9.8

m s

^{-2}

. The water is treated as a uniform inviscid continuum, the surface waves as of small amplitude, and the water as deep compared with their wavelength. ((a)) Chapter 11's Froude number for a hull is

Fr = U/\sqrt{gL}

. Evaluate it. ((b)) Chapter 12 gives the phase speed of a small-amplitude deep-water gravity wave of wavelength

\lambda

c_w = \sqrt{g\lambda/(2\pi)}

. Find the wavelength of the wave whose phase speed equals the speed of the launch. ((c)) Find the speed of sound in the seawater. ((d)) Evaluate the Mach number of the water flowing past the hull, and the fractional density change

\Delta\rho/\rho_0 \approx Ma^{2}/2

at the stagnation point on the bow. Say whether the water may be treated as of constant density.

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