A U-tube open at both ends is partially filled with water (Figure a). Oil having
ID: 2263204 • Letter: A
Question
A U-tube open at both ends is partially filled with water (Figure a). Oil having a density of 805 kg/m3 is then poured into the right arm and forms a column L = 4.90 cm high (Figure b).
(a) Determine the difference h in the heights of the two liquid surfaces.
(b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Figure c). Determine the speed of the air being blown across the left arm. Take the density of air as 1.20 kg/m3.
A U-tube open at both ends is partially filled with water (Figure a). Oil having a density of 805 kg/m3 is then poured into the right arm and forms a column L = 4.90 cm high (Figure b). Determine the difference h in the heights of the two liquid surfaces. The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Figure c). Determine the speed of the air being blown across the left arm. Take the density of air as 1.20 kg/m3.Explanation / Answer
a) density of water=1000kg/m3
oil density=805kg/m3
now pressure at the level where oil meets water has to be the same in both arms of the u tube. so,
density of water*g*(L-h)=density of oil*g*(L)
1000(L-h)=805L
195L=1000h
h=195*4.9/1000=0.955cm
b) water in the left arm is raised by a height of h/2 for the levels to be equal on both sides. so the amount of pressure difference created by the air flow has to be equal to the pressure due to h/2 height of column
so,
1000*g*h/2=0.5*d*v*v
1000*9.81*0.00955/2=0.5*1.2*v*v
v^2=78.07125
v=8.835m/s
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