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

See similar textbooks

Similar questions

Differantial Equations
Topic : Mixture Flow Problem A tank initially holds 100 gal of salt solution in which 50 Ib of salt has been dissolved. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lb of dissolved salt per gallon. Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank at 2pm. Find the amount of salt at the end of 30 minutes. Ans. 171.24 Ib
Distilled water at 10deg C stands in a glass tube of 9.0 mm diameter at a height of 24.00 mm. What is the true static height in mm if the surface tesnsion is 0.0742 N/m. a.24 mm b.27.4 mm c.20.6 mm d.3.4 mm
Q1: Mass flow through a sonic nozzle is a function of gas pressure and temperature (Pressure = P, Temperature = T). If the mass flow rate through the nozzle is given by: m = 0.0430 70.5 Where: m Ib/min, P = Psia, T = °R a) Determine what the units for the constant 0.0430 are? b) What will be the new value of the constant, now gives as 0.0430, if the variables in the equation are to be substituted with SI units and m is calculated in SI units? Q2: Some of fermentation organism which is used to analyze the waste water from oil refinery can live at reduced air pressure down to 22 Kpa. In a test a mercury manometer attached to a tank reads 64.5 cmHg and the barometer reads 104 Kpa. Will the organize live at this conditions?
i) hovzontal pos 80°C air cokulate the rate of heat tr in the cauity per unit depth
b) Table 2 shows the free delivery and shut off points of the individual data for pump A, B and C. Suggest the order of pump that needs to be shut off if all pumps are arranged in series. Table 2 Individual pump free delivery and shut off data. Free delivery (m³/s) Shut off (m) Pump A 20 4 Pump B 15 6. Pump C 35
At a pressure of 0.01 atm, determine (a) the melting temperature for ice, and (b) the boiling temperature for water. You might want to use Animated Figure. (a) i °C (b) і °C
What would be the rotation rate (in rad/sec) if during rotation the water in the right leg (with a diameter of d) decreases a distance h1=0.11 m? A U-tube Elevation = 20 cm 20 cm 2d Elevation = 0 -20 cm- B +20 cm A
THERMODYNAMICS UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS/DIAGRAMS LEGIBLY. NO LONG EXPLANATION NEEDED. USE 3 DECIMAL PLACES. BOX THE FINAL ANSWER. A pump discharges into a semi spherical tank at the bottom and cylindrical on top with a radius of 2 meters, and a total tank height of 8 meters. The flow rate is 80 gallons per minute and fluid specific gravity= 1.1. Determine the following: D.) how many drums will be needed to transfer all of the tank contents (tank being full) to the drums?
As an environmental engineer working for a consulting company you were asked to evaluate an existing water treatment plant for possible upgrade. One of the treatment unit processes you evaluated was the rapid mix tank. You had the following information. 2. Current average water flow rate 15 x 10' m'/d. Projected flow rate in 20 years 24 x 10' m'/d. Temperature of water varies from 12 to 20° C. No. of rapid mix tank = 1 Dimension of tank: water depth 2.1 m, width 2.1 m, length 2.1 m Tank is not baffled: Mixer is 4-bladed turbine with 45° pitched blade (N, = 1.27) Diameter of impeller 0.9 m Label on the motor: horsepower of motor 10 hp (1 hp 746 watts) rpm of blades = 120 rpm (assume a motor efficiency of 80%) Evaluate whether the rapid mix system (1) Is sufficiently designed for current use? If not, provide some remedies. (i) Will the current system be sufficient for the projected flow rate in 20 years? If not, what are some of your suggestions or additions to meet the projected flow?
20. Calculate the pressure at a height of 8000 m above sea-level if the atmospheric pressure is 101.3 kN/m² and temperature is 15°C at the sea-level assuming (i) air is incompressible, (ii) pressure variation follows adiabatic law, and (iii) pressure variation follows isothermal law. Take the density of air at the sea-level equal to 1.285 kg/m³. Neglect variation of gwith altitude. [Ans. (i) 607.5 N/m², (ii) 31.5 kN/m² (iji) 37 45 kN/m² 1
THERMODYNAMICS UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS/DIAGRAMS LEGIBLY. NO LONG EXPLANATION NEEDED. USE 3 DECIMAL PLACES. BOX THE FINAL ANSWER. A pump discharges into a semi spherical tank at the bottom and cylindrical on top with a radius of 2 meters, and a total tank height of 8 meters. The flow rate is 80 gallons per minute and fluid specific gravity= 1.1. Determine the following: A) flow rate in kg/sec and time it takes to fill the tank in hours. Flow Rate and Time