The single tank system (Figure 1) has been modelled by the first order differential equation given as equation 1. The equation describes the relationship between the input flow rate entering the tank and the head of liquid in the tank. Qin = A dh + dt R po h R equation 1 The following constants are provided: R = 40 Kpa s m²³, A = 10 m², p = 1001 kg m³, and g = 9.81 m s²2 A pump is suddenly switched on and provides a step input flow rate of 0.5 m³ s¹. (i) Using Laplace Transforms, solve equation and provide an expression to show how the level in the tank will vary in time after the step input has been applied.

The single tank system (Figure 1) has been modelled by the first order differential equation given as equation 1. The equation describes the relationship between the input flow rate entering the tank and the head of liquid in the tank. Qin = A dh + dt R po h R equation 1 The following constants are provided: R = 40 Kpa s m²³, A = 10 m², p = 1001 kg m³, and g = 9.81 m s²2 A pump is suddenly switched on and provides a step input flow rate of 0.5 m³ s¹. (i) Using Laplace Transforms, solve equation and provide an expression to show how the level in the tank will vary in time after the step input has been applied.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

The single tank system (Figure 1) has been modelled by the first order differential equation given as
equation 1. The equation describes the relationship between the input flow rate entering the tank and the
head of liquid in the tank.
Qin
=
dh pg
A- + h
dt R
equation (1
The following constants are provided:
R = 40 Kpa s m³³, A = 10 m², p= 1001 kg m³, and g = 9.81 m s²2
A pump is suddenly switched on and provides a step input flow rate of 0.5 m³ s¹.
(i) Using Laplace Transforms, solve equation and provide an expression to show how the level in
the tank will vary in time after the step input has been applied.

'p' (liquid
density)
'A' (tank cross
sectional area)
'Qin' (Input Flow Rate)
Qout'
P
Figure 1
'h' (head
of liquid)
'R' (restriction coefficient)
5m

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