A U-tube with horizontal base of length 'l' holds equal volumes of two non-mixing liquids of densities rho and 2rho. The tube is accelerated horizontally with acceleration 'a'. If the levels in the two open arms come to the same height, find the height h of the heavier liquid column.

Question

Accepted Answer

3al/2g. Equal volumes of the two liquids fill the tube. With the free surfaces brought to the same level, balancing the horizontal pseudo-force pressure along the base against the difference in the liquid columns gives the required height. Carrying out the pressure balance for densities rho and 2rho over base length l yields h = 3al/2g.

A U-tube with horizontal base of length 'l' holds equal volumes of two non-mixing liquids of densities rho and 2rho. The tube is accelerated horizontally with acceleration 'a'. If the levels in the two open arms come to the same height, find the height h of the heavier liquid column.

Solution

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