A U -tube open at both ends is partially filled with water (Fig. a). Oil ( = 670

Question

A U-tube open at both ends is partially filled with water (Fig. a). Oil ( = 670 kg/m3) is then poured into the right arm and forms a column L = 6.2 cm high (Fig. b).

(a) Determine the difference h in the heights of the two liquid surfaces. (cm)

(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 (Fig. c). Determine the speed of the air being blown across the left arm. Assume that the density of air is 1.29 kg/m3. (m/s)

Explanation / Answer

:  a) density *g*height of the oil = density *g*h of the water

so 670*6.2cm = 1000*h

so h of water =( 670/1000)*6.2cm

   = 0.67 *6.2 = 4.154cm

so the difference = 6.2- 4.154 = 2.046cm

b) The gauge pressure of the in the tube

= *g*h = 670kg/m^3*9.8m/s^2*0.062m = 407.092Pa

So the dynamic pressure must equal this value

Therefore 1/2**v^2 = 407.092

So v = sqrt(2*407.092/1.29) = 25.12m/s

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