Finding Hydrostatic Pressure in Water that is Isothermal

Melamed555 · September 11, 2018, 11:33

I am an engineering student and I was given a problem to find the pressure at a certain depth. I was given a surface density and a bulk modulus of elasticity. My professor said that we should be incorporating a speed of sound equation to help us find the answer. I solved for the speed of sound correctly and I am assuming that to be constant because of the isothermal assumption. The water is assumed to be compressible so I am having trouble finding the new density. Could someone give me some advice on how to go about starting this? I didn't include the values because I am not looking for the answer. I would prefer to figure that out on my own.

Thanks in advance

FMDenaro · September 11, 2018, 11:53

Be careful about the "compressibility" in water, the pressure increases along the depth as a result of the weight of the above mass of liquid. But we do not have variation of volume.

agd · September 11, 2018, 13:37

It sounds to me like you might need to refer back to the fundamental definition of the sound speed as the partial derivative of pressure with respect to density at constant density. A little manipulation can give (for a fluid like water) that this is the derivative of pressure with respect to density at constant temperature. If you assume that the speed of sound is constant, then you can integrate to get a relation between density and pressure.

September 11, 2018, 11:33	Finding Hydrostatic Pressure in Water that is Isothermal	#1
Melamed555 New Member Ziv Melamed Join Date: Sep 2018 Posts: 1 Rep Power: 0	I am an engineering student and I was given a problem to find the pressure at a certain depth. I was given a surface density and a bulk modulus of elasticity. My professor said that we should be incorporating a speed of sound equation to help us find the answer. I solved for the speed of sound correctly and I am assuming that to be constant because of the isothermal assumption. The water is assumed to be compressible so I am having trouble finding the new density. Could someone give me some advice on how to go about starting this? I didn't include the values because I am not looking for the answer. I would prefer to figure that out on my own. Thanks in advance

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September 11, 2018, 11:53		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	Be careful about the "compressibility" in water, the pressure increases along the depth as a result of the weight of the above mass of liquid. But we do not have variation of volume.

September 11, 2018, 13:37		#3
agd Senior Member Join Date: Jul 2009 Posts: 353 Rep Power: 18	It sounds to me like you might need to refer back to the fundamental definition of the sound speed as the partial derivative of pressure with respect to density at constant density. A little manipulation can give (for a fluid like water) that this is the derivative of pressure with respect to density at constant temperature. If you assume that the speed of sound is constant, then you can integrate to get a relation between density and pressure.