Explanation Consider the steam flows at steady state. Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 = m ˙ Write the energy rate balance equation for one inlet and one outlet system. [ Q ˙ 1 + W ˙ 1 + m ˙ ( h 1 + V 1 2 2 + g z 1 ) ] − [ Q ˙ 2 + W ˙ 2 + m ˙ ( h 2 + V 2 2 2 + g z 2 ) ] = Δ E ˙ system (I) Here, the rate of heat transfer is Q ˙ , the rate of work transfer is W ˙ , the enthalpy is h and the velocity is V , the gravitational acceleration is g , the elevation from the datum is z and the rate of change in net energy of the system is Δ E ˙ system ; the suffixes 1 and 2 indicates the inlet and outlet of the system. The system is at steady state. Hence, the rate of change in net energy of the system becomes zero. Δ E ˙ system = 0 Here, the pipe is insulated, neglect the heat transfer i.e. Q ˙ 1 = Q ˙ 2 = 0 . Also neglect the kinetic and potential energy changes. No work is involved, neglect the work transfers. The Equations (II) reduced as follows. [ 0 + 0 + m ˙ ( h 1 + 0 + 0 ) ] − [ 0 + 0 + m ˙ ( h 2 + 0 + 0 ) ] = 0 m ˙ h 1 − m ˙ h 2 = 0 m ˙ h 1 = m ˙ h 2 h 1 = h 2 (II) Write the formula for inlet and outlet mass flow rates. Inlet flow rate m ˙ = m ˙ 1 = A 1 V 1 v 1 = ( π D 1 2 4 ) V 1 v 1 (III) Outlet flow rate m ˙ = m ˙ 2 = A 2 V 2 v 2 = ( π D 2 2 4 ) V 2 v 2 (IV) Here, the cross-sectional area is A , the diameter of the pipe is D , the velocity is V and the specific volume is V ; the suffixes 1 and 2 indicates the inlet and outlet conditions. Rearrange the Equation (IV) to obtain the exit velocity ( V 2 ) . V 2 = m ˙ v 2 A 2 = m ˙ v 2 ( π D 2 2 4 ) = 4 m ˙ v 2 π D 2 2 (V) Refer Table A-6, “Superheated water”

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Chapter 5.5, Problem 147RP

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The mass flow rate of steam and its speed at the pipe outlet.

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Chapter 5.5, Problem 146RP

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The mass flow rate of steam and its speed at the pipe outlet.

Solution Summary: The author explains the mass flow rate of steam and its velocity at the pipe outlet. The energy rate balance equation is for one inlet and one outlet system.

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The mass flow rate of steam and its speed at the pipe outlet.

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