Water flows in and out of the device as shown. Calculate the rate of change of t
ID: 1829220 • Letter: W
Question
Water flows in and out of the device as shown. Calculate the rate of change of the mass of water (dm/dt) in the device. Hint: This problem makes use of conservation of mass within the control volume framework (see notes). Note that rho Q2 = 20 kg/s in the direction shown. (Answer: Mass is decreasing at a rate of 14.9 kg/s) Determine the rate at which the water level increases or decreases in an open container if the water coming in through a 0.10-m2 pipe has a velocity of 0.5 m/s and the flow rate going out is 0.2 m3/s. The container has a circular cross section with a diameter of 0.5 m. Hint: Same as in problem 1. (Answer: The water level decreases at a rate of 0.764 m/s)Explanation / Answer
1.
dm / dt = m_out - m_in
dm / dt = (m2 + m3) - m1
= 20 + rho*Q3 - rho*A1*V1
= 20 + 1000*0.01 - 1000*(3.14*0.04^2 /4)*12
= 14.9 kg/s
2.
A_cyl*(dh/dt) = Q_in - Q_out
(3.14*0.5^2 / 4)*(dh / dt) = A_in*V_in - Q_out
(3.14*0.5^2 / 4)*(dh / dt) = 0.1*0.5 - 0.2
dh / dt = -0.764 m/s (minus sign indicates decreasing water height)
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