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Chapter 6: Problem 116

A pump operating at steady state receives saturated liquid water at \(50^{\circ} \mathrm{C}\) with a mass flow rate of \(20 \mathrm{~kg} / \mathrm{s}\). The pressure of the water at the pump exit is \(1 \mathrm{MPa}\). If the pump operates with negligible internal irreversibilities and negligible changes in kinetic and potential energy, determine the power required in \(\mathrm{kW}\).

Short Answer

Expert verified
Identify properties at 50掳C, use the specific work formula, and compute the power using mass flow rate.

Step by step solution

01

Identify Given Data

List the given data from the problem: \(T_1 = 50^{\circ} \mathrm{C}\), mass flow rate \( \dot{m} = 20 \mathrm{kg}/\mathrm{s}\), and pressure at exit \( P_2 = 1 \mathrm{MPa} \).
02

Find Saturation Properties at \(50^{\circ} \mathrm{C}\)

From the steam tables, find the enthalpy of saturated liquid water at \(50^{\circ} \mathrm{C}\): \( h_1 = h_f(50^{\circ} \mathrm{C}) \).
03

Utilize the Pump's Assumptions

Given the pump operates with negligible internal irreversibilities and changes in kinetic and potential energy, use the specific work of the pump equation: \( w_p = v_1 (P_2 - P_1) \). Here, \( v_1 \) is the specific volume at the inlet.
04

Determine Specific Volume

From the steam tables at \(50^{\circ} \mathrm{C}\), find the specific volume: \( v_1 = v_f(50^{\circ} \mathrm{C}) \).
05

Convert Units and Apply Values

Convert pressure and specific volume units if necessary to ensure consistency. Apply given values into the equation \[ w_p = v_1 (P_2 - P_1) \] .
06

Calculate Power

Multiply specific work by the mass flow rate to find power: \[ W = \dot{m} \, w_p \].
07

Compute Final Answer

Using the values from previous steps, calculate the power required: \[ W = \dot{m} \, v_1 (P_2 - P_1) \]. Ensure the answer is in \(\mathrm{kW} \).

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Key Concepts

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

thermodynamic processes
Thermodynamic processes describe the changes that occur in a system as energy is transferred or transformed. In our problem with the pump, we're looking at a steady-state process involving the flow of water. Steady-state means that properties such as mass flow rate, pressure, and temperature don't change with time. The water enters the pump as a saturated liquid at a specific temperature and exits at a higher pressure. Understanding how the properties of water change during this process is essential for calculating the pump's power requirements.
steam tables
Steam tables are crucial for solving thermodynamic problems. They provide data on properties such as enthalpy, specific volume, and entropy for water and steam at various temperatures and pressures. For our exercise, we used the steam tables to find the enthalpy and specific volume of saturated liquid water at 50掳C. The specific volume is important for calculating the work done by the pump. To find these values, you can look up the saturation properties at 50掳C in the steam tables. The tables are typically divided into sections for saturated liquid, saturated vapor, and superheated vapor.
power calculation
The goal of the problem is to calculate the power required by the pump. The power is the rate at which work is done. To find this, we use the equation for the specific work done by the pump: \[ w_p = v_1 (P_2 - P_1) \] Here, \( v_1 \) is the specific volume of the saturated liquid at the pump inlet, \( P_2 \) is the pressure at the pump exit, and \( P_1 \) is the pressure at the pump inlet. Once the specific work is calculated, we multiply it by the mass flow rate to find the total power: \[ W = \dot{m} \ w_p \] This gives us the power required by the pump in kilowatts (kW). Ensuring that all units are consistent and correct is critical for an accurate calculation.

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Most popular questions from this chapter

If a closed system would undergo an internally reversible process and an irreversible process between the same end states, how would the changes in entropy for the two processes compare? How would the amounts of entropy produced compare?

Using steam table data, determine the indicated property data for a process in which there is no change in specific entropy between state 1 and state \(2 .\) In each case, locate the states on a sketch of the \(T-s\) diagram. (a) \(T_{1}=40^{\circ} \mathrm{C}, x_{1}=100 \%, p_{2}=150 \mathrm{kPa}\). Find \(T_{2}\), in \({ }^{\circ} \mathrm{C}\), and \(\Delta h\), in \(\mathrm{kJ} / \mathrm{kg}\). (b) \(T_{1}=10^{\circ} \mathrm{C}, x_{1}=75 \%, p_{2}=1 \mathrm{MPa}\). Find \(T_{2}\), in \({ }^{\circ} \mathrm{C}\), and \(\Delta u\), in \(\mathrm{kJ} / \mathrm{kg}\).

A counterflow heat exchanger operates at steady state with negligible kinetic and potential energy effects. In one stream, liquid water enters at \(15^{\circ} \mathrm{C}\) and exits at \(23^{\circ} \mathrm{C}\) with a negligible change in pressure. In the other stream, Refrigerant 22 enters at 12 bar, \(90^{\circ} \mathrm{C}\) with a mass flow rate of \(150 \mathrm{~kg} / \mathrm{h}\) and exits at 12 bar, \(28^{\circ} \mathrm{C}\). Heat transfer from the outer surface of the heat exchanger can be ignored. Determine (a) the mass flow rate of the liquid water stream, in \(\mathrm{kg} / \mathrm{h}\). (b) the rate of entropy production within the heat exchanger, in \(\mathrm{kW} / \mathrm{K}\).

Air enters an insulated compressor operating at steady state at 1 bar, \(350 \mathrm{~K}\) with a mass flow rate of \(1 \mathrm{~kg} / \mathrm{s}\) and exits at 4 bar. The isentropic compressor efficiency is \(82 \%\). Determine the power input, in \(\mathrm{kW}\), and the rate of entropy production, in \(\mathrm{kW} / \mathrm{K}\), using the ideal gas model with data from Table A-22.

A rigid tank is filled initially with \(5.0 \mathrm{~kg}\) of air at a pressure of \(0.5 \mathrm{MPa}\) and a temperature of \(500 \mathrm{~K}\). The air is allowed to discharge through a turbine into the atmosphere, developing work until the pressure in the tank has fallen to the atmospheric level of \(0.1 \mathrm{MPa}\). Employing the ideal gas model for the air, determine the maximum theoretical amount of work that could be developed, in \(\mathrm{kJ}\). Ignore heat transfer with the atmosphere and changes in kinetic and potential energy.
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