/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 A feedwater heater operates at s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 65

A feedwater heater operates at steady state with liquid water entering at inlet 1 at 7 bar, \(42^{\circ} \mathrm{C}\), and a mass flow rate of \(70 \mathrm{~kg} / \mathrm{s}\). A separate stream of water enters at inlet 2 as a two-phase liquid-vapor mixture at 7 bar with a quality of \(98 \%\). Saturated liquid at 7 bar exits the feedwater heater at 3. Ignoring heat transfer with the surroundings and neglecting kinetic and potential energy effects, determine the mass flow rate, in \(\mathrm{kg} / \mathrm{s}\). at inlet 2 ,

Short Answer

Expert verified
The mass flow rate at inlet 2 is approximately 18.32 kg/s.

Step by step solution

01

- Identify Known Variables

Identify the given values for the exercise: - Inlet 1: - Pressure, \(P_1 = 7\) bar - Temperature, \(T_1 = 42^{\bullet}C\) - Mass Flow Rate, \( \dot{m}_1 = 70 ~ kg/s \)- Inlet 2: - Pressure, \(P_2 = 7\) bar - Quality, \(x_2 = 0.98 \)- Outlet (State 3): - Pressure, \(P_3 = 7\) bar (Saturated Liquid)
02

- Determine Enthalpies

To find the enthalpy values, use steam tables.For Inlet 1: - \(h_1 = 179.9 ~ kJ/kg\) (for liquid water at 7 bar and 42掳C)For Inlet 2: - Find \(h_f\) and \(h_fg\) at 7 bar from the steam tables. - \(h_f = 697.2 ~ kJ/kg\) - \(h_fg = 2030.3 ~ kJ/kg\) - Calculate \( h_2 \) using the quality: \[ h_2 = h_f + x_2 h_fg = 697.2 + (0.98 \times 2030.3) = 2673.5~ kJ/kg \]For State 3 (Saturated Liquid at 7 bar): - \(h_3 = h_f = 697.2 ~ kJ/kg\)
03

- Apply Mass and Energy Balances

Since the system is in a steady state and there is no heat transfer with the surroundings, the mass and energy balances are as follows:Mass Balance: - \( \dot{m}_1 + \dot{m}_2 = \dot{m}_3 \)Energy Balance: - \( \dot{m}_1 h_1 + \dot{m}_2 h_2 = \dot{m}_3 h_3 \)
04

- Express Mass Balance in Terms of Mass Flow Rates

Since the exit stream is a combination of both inlets, the mass balance equation becomes:\[ \dot{m}_3 = \dot{m}_1 + \dot{m}_2 \]
05

- Solve for Mass Flow Rate at Inlet 2

First, find \( \dot{m}_3 \) using the energy balance equation:\[ \dot{m}_1 h_1 + \dot{m}_2 h_2 = (\dot{m}_1 + \dot{m}_2) h_3 \]Rearrange to solve for \( \dot{m}_2 \):\[ \dot{m}_2 (h_2 - h_3) = \dot{m}_1 (h_3 - h_1) \]\[ \dot{m}_2 = \frac{\dot{m}_1 (h_3 - h_1)}{h_2 - h_3} \]Substitute the values:\[ \dot{m}_2 = \frac{70 ~kg/s (697.2 - 179.9)~kJ/kg}{2673.5 - 697.2} ~kJ/kg \]\[ \dot{m}_2 = \frac{70 \times 517.3}{1976.3} \dot{m}_2 = 18.32 ~kg/s \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

steady state process
In thermodynamic systems, a steady state process means that the properties of the system do not change with time. This implies that the variables such as pressure, temperature, and mass flow rates are constant during the observation period. In the context of the feedwater heater problem, this means that the mass flow entering the heater equals the mass flow exiting it. Importantly, since the process is steady state, we assume no accumulation of mass or energy in the system. This helps simplify our mass and energy balance equations.
enthalpy calculation
Enthalpy is a measure of the total energy of a thermodynamic system, and it includes both internal energy and the energy required to make room for it by displacing its environment. To solve the feedwater heater problem, we need to calculate the enthalpy at different states using steam tables:

For inlet 1, with given pressure and temperature, the enthalpy (\(h_1\)) is directly looked up from the steam tables for water at 7 bar and 42掳C.
For inlet 2, a two-phase mixture at 7 bar with a quality of 98%, we use the formula: \[ h_2 = h_f + x_2 h_fg \] Here, \(h_f\) is the enthalpy of saturated liquid and \(h_fg\) is the enthalpy change from liquid to vapor at the given pressure.
For outlet 3, which is saturated liquid at 7 bar, the enthalpy (\(h_3\)) is simply the enthalpy of the saturated liquid at 7 bar, i.e., \(h_f\).
mass and energy balances
In the steady state operation of the feedwater heater, the principle of conservation of mass and energy applies.

**Mass Balance Equation:**
Since the system is said to have no mass accumulation, the mass entering the heater must equal the mass leaving:
\[\dot{m}_1 + \dot{m}_2 = \dot{m}_3\]
**Energy Balance Equation:**
Similarly, since there is no heat transfer with the surroundings and ignoring kinetic and potential energy effects, the energy entering must equal the energy leaving:
\[\dot{m}_1 h_1 + \dot{m}_2 h_2 = \dot{m}_3 h_3\]
With the mass flow rates and enthalpies defined, these equations can be used to determine unknown variables such as the mass flow rate at inlet 2.
steam tables
Steam tables are an essential tool in thermodynamics and are used to find the properties of water and steam at various temperatures and pressures. For the feedwater heater problem, steam tables are used to find:

- The enthalpy (\(h_1\:and\:h_3\)) of water and saturated liquid at 7 bar.
- The enthalpy (\(h_f\:and\:h_fg\)) values for calculating the enthalpy of the two-phase mixture at inlet 2.

Using steam tables simplifies the calculation process since the needed thermodynamic properties are pre-tabulated for quick reference based on pressure and temperature. This allows for an accurate determination of enthalpies, which are crucial for solving mass and energy balances accurately.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Liquid propane enters an initially empty cylindrical storage tank at a mass flow rate of \(10 \mathrm{~kg} / \mathrm{s}\). The tank is 25 -m long and has a 4-m diameter. The density of the liquid propane is \(450 \mathrm{~kg} / \mathrm{m}^{3}\). Determine the time, in \(\mathrm{h}\), to fill the tank.

Ammonia enters a refrigeration system compressor operating at steady state at \(-18^{\circ} \mathrm{C}, 138 \mathrm{kPa}\), and exits at \(150^{\circ} \mathrm{C}, 1724 \mathrm{kPa}\). The magnitude of the power input to the compressor is \(7.5 \mathrm{~kW}\), and there is heat transfer from the compressor to the surroundings at a rate of \(0.15 \mathrm{~kW}\). Kinetic and potential energy effects are negligible. Determine the inlet volumetric flow rate, in \(\mathrm{m}^{3} / \mathrm{s}\), first using data from Table A-15, and then assuming ideal gas behavior for the ammonia. Discuss.

A tank contains \(500 \mathrm{~kg}\) of liquid water. The tank is fitted with two inlet pipes, and the water is entering through these pipes at the mass flow rates of \(0.6 \mathrm{~kg} / \mathrm{s}\) and \(0.7 \mathrm{~kg} / \mathrm{s}\). It has one exit pipe through which water is leaving at a mass flow rate of \(1 \mathrm{~kg} / \mathrm{s}\). Determine the amount of water that will be left in the tank after twenty minutes.

A cylindrical tank contains \(1500 \mathrm{~kg}\) of liquid water. It has one inlet pipe through which water is entering at a mass flow rate of \(1.2 \mathrm{~kg} / \mathrm{s}\). The tank is fitted with two outlet pipes and the water is flowing through these exit pipes at the mass flow rates of \(0.5 \mathrm{~kg} / \mathrm{s}\) and \(0.8 \mathrm{~kg} / \mathrm{s}\). Determine the amount of water that will be left in the tank after thirty minutes.

Shows a mixing tank initially containing \(1500 \mathrm{~kg}\) of liquid water. The tank is fitted with two inlet pipes, one delivering hot water at a mass flow rate of \(0.5 \mathrm{~kg} / \mathrm{s}\) and the other delivering cold water at a mass flow rate of \(0.8 \mathrm{~kg} / \mathrm{s}\). Water exits through a single exit pipe at a mass flow rate of \(1.4 \mathrm{~kg} / \mathrm{s}\) Determine the amount of water, in \(\mathrm{kg}\), in the tank after one hour.
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Fields in Physics

Read Explanation

Mechanics and Materials

Read Explanation

Scientific Method Physics

Read Explanation

Electricity

Read Explanation

Thermodynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.