Fluid Sea water is often modeled as an incompressible fluid with a density of rh

Question

Fluid

Sea water is often modeled as an incompressible fluid with a density of rho = 1025 kg m-3. What is the pressure at the bottom of the Mariana Trench at a depth of 10.971 m? Assume constant density fluid and atmospheric pressure at the surface (Po = 101 kPa). However, sea water is not an incompressible fluid. Its density can be approximated as: rho(P) = rho 0[1 + beta (P - P0)] where beta is the fluid compressibility (beta = 4.6 middot 10-10 Pa-1) What would the pressure be at the bottom of the Mariana Trench using this more accurate density model? Answer hint: 110.4 MPa, 113.3 MPa

Explanation / Answer

P = P0 + rho*g*h

P = 101000+1025*9.81*10971

P = 110417147.8

P = 110.4 Mpa

if ,

density is not constant,

P = 101000+ 1025*(1+4.6*10^-10(P-101000))

solving it,

P = 113.3 Mpa

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