(a) To determine The mass of the oil in the tank in kg after 24 hours. Explanation Write the equation for mass rate balance ( d m cv d t ) in the tank (time rate of change of mass). d m cv d t = m ˙ 1 − m ˙ 2 . (I) Write the formula for mass flow rate ( m ˙ 1 ) of crude oil at inlet. m ˙ 1 = ( AV ) 1 v (II) Here, the volume flow rate at the inlet is ( AV ) 1 and the specific volume of crude oil is v . Write the formula for mass flow rate ( m ˙ 2 ) of crude oil at exit. m ˙ 2 = A 2 V 2 v (III) Here, the cross sectional area at exit pipe is A 2 and the exit velocity is V 2 . Write the formula for exit pipe cross-sectional area ( A 2 ) . A 2 = π d 2 4 (IV) Here, the diameter of the pipe is d . Integrate d m cv from Equation (I) at the limits of m initial to m final . ∫ m initial m final d m cv = [ m cv ] m initial m final = m final − m initial Substitute m final − m initial for d m cv in Equation (I) m final − m initial d t = m ˙ 1 − m ˙ 2 m final − m initial = ( m ˙ 1 − m ˙ 2 ) d t (V) Here, the change in time is d t ; m initial and m final are the initial and final masses respectively. Write the formula to calculate the initial mass of the crude oil. m initial = V v (VI) Here, the initial volume of oil in the tank is V . Conclusion: Substitute 2 m 3 / min for ( AV ) 1 and 0 .0015 m 3 /kg for v in Equation (II). m ˙ 1 = 2 m 3 / min 0 .0015 m 3 /kg = 2 m 3 min × 60 min 1 h 0 (b) To determine The volume of the oil in the tank in m 3 after 24 hours.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 4.12, Problem 10P

(a)

To determine

The mass of the oil in the tank in kg after 24 hours.

(b)

To determine

The volume of the oil in the tank in m3 after 24 hours.

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Chapter 4.12, Problem 9P

Chapter 4.12, Problem 11P

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