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Develop the dynamic mathematical model relating the change of liquid depth h with respect to time t. The derivative term should be expressed as dh/dt. Express the angle 0 in terms of the tank geometry. Consider the dependency on the inlet flow rate with respect to time as an independent variable. Do not attempt to solve the resulting mathematical model.

Develop the dynamic mathematical model relating the change of liquid depth h with respect to time t. The derivative term should be expressed as dh/dt. Express the angle 0 in terms of the tank geometry. Consider the dependency on the inlet flow rate with respect to time as an independent variable. Do not attempt to solve the resulting mathematical model.

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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Consider a conical tank of maximum radius R at maximum liquid depth H. Liquid flows into the tank at volumetric rate F, and leaves at volumetric rate F₁. Flow through the outlet valve has linear flow characteristics as given by the following equation: F₁ = C₁.h Evaporative losses at the surface are proportional to the surface area. Assume the liquid density remains constant. H R F₁ Develop the dynamic mathematical model relating the change of liquid depth h with respect to time t. The derivative term should be expressed as dh/dt. Express the angle in terms of the tank geometry. Consider the dependency on the inlet flow rate with respect to time as an independent variable. Do not attempt to solve the resulting mathematical model.
Transcribed Image Text:Consider a conical tank of maximum radius R at maximum liquid depth H. Liquid flows into the tank at volumetric rate F, and leaves at volumetric rate F₁. Flow through the outlet valve has linear flow characteristics as given by the following equation: F₁ = C₁.h Evaporative losses at the surface are proportional to the surface area. Assume the liquid density remains constant. H R F₁ Develop the dynamic mathematical model relating the change of liquid depth h with respect to time t. The derivative term should be expressed as dh/dt. Express the angle in terms of the tank geometry. Consider the dependency on the inlet flow rate with respect to time as an independent variable. Do not attempt to solve the resulting mathematical model.
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