Physics Help Forum Question on Fluids and Pressure

 Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum

 Mar 9th 2009, 11:29 PM #1 Senior Member   Join Date: Feb 2009 Location: Singapore Posts: 206 Question on Fluids and Pressure A hydrometer floats in water with 6.0cm of its stem above the water level, and in oil of density 0.8gcm^-3 with 4.0 cm of its stem above the oil level. What is the length of the stem above the water level when the hydrometer is placed in a liquid of density 0.9gcm^-3? I used the weight, and height of above the water level to determine the total length of the hydrometer, then used it to solve for the height above the liquid level in the last part. and got an answer to 0.6mm of the answer, i wonder if it is calculation error or method error.
 Mar 10th 2009, 01:28 AM #2 Physics Team   Join Date: Feb 2009 Posts: 1,425 The weight of the hydrometer = weight of vol of liquid displaced (Archimedes principle). Let m be the mass , L be the length , and A be the cross sectional area of the hydrometer. Let d1, d2 , d3 be the densities of the liquids and x1, x2, x3 be the length of the stem above the water level . We have mg = d1(L-x1) A g = d2(L-x2) A g = d3(L-x3) A g. Note that the area cancels out. Now plug in the values and solve. I got L = 14 and x3 = 5.111 cm
 Mar 10th 2009, 01:44 AM #3 Senior Member   Join Date: Feb 2009 Location: Singapore Posts: 206 i got that same number, but the answer in the book is 5.17cm do you think the book got it wrong?
 Mar 10th 2009, 05:31 AM #4 Physics Team   Join Date: Feb 2009 Posts: 1,425 I think they have got it wrong or else have they used density of water as slightly less than 1?
 Mar 10th 2009, 09:19 PM #5 Senior Member   Join Date: Feb 2009 Location: Singapore Posts: 206 i see ok thanks

 Tags fluids, pressure, question