U-tube manometer fluid mechanics

AI Thread Summary
The discussion centers on a problem involving a U-tube manometer filled with water and oil, where the user seeks to determine the pressure difference required to move the oil/water interface by 1 cm. The original calculation yielded a pressure difference of 16.67 Pa, while the book's answer is 21 Pa. Participants emphasize the importance of accurately accounting for the changing heights of the liquids in the enlarged sections of the tube, which significantly impacts the pressure difference. They caution against making assumptions without a proper diagram, as this can lead to incorrect conclusions. Accurate visualization and consideration of all variables are crucial for solving fluid mechanics problems effectively.
Iclaudius
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Hi friends - I'm at a lost on this particular problem which reads:

a manometer consists of a U-tube, 7mm internal diameter, with vertical limbs with an enlarged upper end of 44mm diameter. the left-hand limb and the bottom of the tube are filled with water and the top of the right hand limb is filled with oil of specific gravity 0.83. the free surfaces of the liquids are in the enlarged ends and the interface between the oil and water is in the tube below the enlarged end. what would be the difference in pressures applied to the free surfaces which would cause the oil/water interface to move 1cm?

My attempt was to identify all the different pressures that need be accounted for so i ended up with the following equation,

P(left) -P(right) = p(oil) g* 0.01 - p(water) g *0.01

= 16.67 Pa, however answer in book is 21 Pa.

any advice or help would be greatly appreciated,
Claudius
 
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If the OP had drawn a diagram of what is happening, he would have realized that the heights of the liquids in the enlarged sections also change which affects the pressure difference. Guessing an equation is always a bad idea.
 
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