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A tank having a cross-sectional area of 2 ft is operating at steady state with an inlet flow rate of 2.0 cfm. The flow-head characteristics are shown in Fig. P5-3. (a) Find the transfer function H(s)/Q(s). (b) If the flow to the tank increases from 2.0 to 2.2 cfm according to a step change, calculate the level h two minutes after the change occurs.

A tank having a cross-sectional area of 2 ft is operating at steady state with an inlet flow rate of 2.0 cfm. The flow-head characteristics are shown in Fig. P5-3. (a) Find the transfer function H(s)/Q(s). (b) If the flow to the tank increases from 2.0 to 2.2 cfm according to a step change, calculate the level h two minutes after the change occurs.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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solve only (5.3) correct solution plz
PROBLEMS 5.1. Derive the transfer function H(s)/Q(s) for the liquid-level system of Fig. P5-1 when (a) The tank level operates about the steady-state value of h, = 1 ft (b) The tank level operates about the steady-state value of h, = 3 ft q. ft'/min The pump removes water at a constant rate of 10 cfm (cubic feet per minute); this rate is inde- pendent of head. The cross-sectional area of the tank is 1.0 ft, and the resistance Ris 0.5 f/cfm. 5.2. A liquid-level system, such as the one shown in Fig. 5-1, has a cross-sectional area of 3.0 f². The h(1) 2 ft valve characteristics are FIGURE P5-1 AOutlet flow where q = flow rate, cfm, and h = level above the valve, ft. Calculate the time constant for this system if the average operating level above the valve is 2.4 (a) 3 ft (b) 9 ft 5.3. A tank having a cross-sectional area of 2 ft is operating at steady state with an inlet flow rate of 2.0 cfm. The flow-head characteristics are shown 1.0 --- 0.3 1.0 h(ft) in Fig. P5-3. (a) Find the transfer function H(s)/Q(s). (b) If the flow to the tank increases from 2.0 to 2.2 cfm according to a step change, calculate the level h two minutes after the change occurs. FIGURE P5-3 5.4. Develop a formula for finding the time constant of the liquid-level system shown in Fig. P5–4 when the average operating level is ho. The resistance R is linear. The tank has three vertical walls and one that slopes at an angle a from the vertical as shown. The distance separating the parallel walls R ----B- FIGURE P5-4 is 1. 9, (ft/min)
Transcribed Image Text:PROBLEMS 5.1. Derive the transfer function H(s)/Q(s) for the liquid-level system of Fig. P5-1 when (a) The tank level operates about the steady-state value of h, = 1 ft (b) The tank level operates about the steady-state value of h, = 3 ft q. ft'/min The pump removes water at a constant rate of 10 cfm (cubic feet per minute); this rate is inde- pendent of head. The cross-sectional area of the tank is 1.0 ft, and the resistance Ris 0.5 f/cfm. 5.2. A liquid-level system, such as the one shown in Fig. 5-1, has a cross-sectional area of 3.0 f². The h(1) 2 ft valve characteristics are FIGURE P5-1 AOutlet flow where q = flow rate, cfm, and h = level above the valve, ft. Calculate the time constant for this system if the average operating level above the valve is 2.4 (a) 3 ft (b) 9 ft 5.3. A tank having a cross-sectional area of 2 ft is operating at steady state with an inlet flow rate of 2.0 cfm. The flow-head characteristics are shown 1.0 --- 0.3 1.0 h(ft) in Fig. P5-3. (a) Find the transfer function H(s)/Q(s). (b) If the flow to the tank increases from 2.0 to 2.2 cfm according to a step change, calculate the level h two minutes after the change occurs. FIGURE P5-3 5.4. Develop a formula for finding the time constant of the liquid-level system shown in Fig. P5–4 when the average operating level is ho. The resistance R is linear. The tank has three vertical walls and one that slopes at an angle a from the vertical as shown. The distance separating the parallel walls R ----B- FIGURE P5-4 is 1. 9, (ft/min)
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