A large tank of water has a hose connected to it, as shown in the figure (Figure

Question

A large tank of water has a hose connected to it, as shown in the figure (Figure 1) . The tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the value 3.50 m , the absolute pressure p of the compressed air is 4.20 ×105Pa. Assume that the air above the water expands at constant temperature, and take the atmospheric pressure to be 1.00 ×105Pa.

A. As water flows out of the tank, h decreases. Calculate the speed of flow for h= 3.00 m .

B. Calculate the speed of flow for h =2.10 m .

C. At what value of h does the flow stop?

Explanation / Answer

b)

P1 + density * g * h + 0.5 * density * v1^2 = P2 * density * g * 0 + 0.5 * density * v2^2

v2 = sqrt( 2 * (g * h + (P1 - P2) / density)

v2 = sqrt( 2 * ( 9.8 * 3 + (420000 - 100000) / 1000))

v2 = 26.43 m/s

b)

P1 + density * g * h + 0.5 * density * v1^2 = P2 * density * g * 0 + 0.5 * density * v2^2

v2 = sqrt( 2 * (g * h + (P1 - P2) / density)

v2 = sqrt( 2 * ( 9.8 * 2.1 + (420000 - 100000) / 1000))

v2 = 26.09 m/s

c)

P1 * v = n * R * T

and v = A1 * ( H- h )

P1 * (H - h ) = n * R * T / A1 = constant = 420 kPa * ( 0.5) = 210 k Pa

so

v2(h) = sqrt( 2 * ( g * h + ( 210 kPa/(H-h) - 100 kPa) / density)

0 = sqrt( 20 * ( -10 + h + 22 / (4-h))

h = 1.43 m

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