System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 7, Problem 7.2P
Refer to the water storage and supply system shown in Figure 7.1.2. The cylindrical tank has a radius of 11 ft, and the water height is initially 5 ft. Find the water height after 5 hr if 1000 gallons per minute are pumped out of the well and 800 gallons per minute are withdrawn from the tank. Note that 1 gallon is 0.13368 ft3.
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1. A pipe with a radius of 0.1 m used to drain an entire full water tank within one
hour. The tank is a cylinder with a height (h) of 3 meters and a diameter of 5 meters.How fast will the water need to move through the pipe? Draw an illustration that will help you visualize the problem. Indicate important labels and measurements in your illustration.
After completing the ENGR 315 hands-on project Sparky decided to create a symbolic solution for the time it takes for water to drain from the bottle. Sparky will compare the times to a YouTube video of the hands-on project. Sparky’s bottle is 4 inches in diameter and contains three holes of equal size (not what was required by the hands-on experiment). The hole size of diameter (dhole) is in inches and the holes are L inches apart. There is Ltop inches was water above the top hole at the start of the experiment (as shown in the figure). Neglecting viscous effects (orifice coefficient) and considering the flow conditions to be quasi-steady (consistent with the hands-on experiment) create a symbolic solution for the time it takes for water to stop draining from the top hole. The density (ρ) and specific weight (γ) of the water are 1.94 slugs/ft3 and 62.4 lbf/ft3, respectively. The height of water above the first hole is h, which varies with time. The flow through each hole is the…
Task 3
Gas, evolved as a result of a chemical reaction, sequentially flows
from the retort A into the vessels B and C and into the collector D. The
vessels B and C are filled by cleansing solution (densities: pg=1003
kg/m³,pc=1005 kg/m3), the collector D is filled by water (density
Pp=1000 kg/m³). The geometric dimensions given in the figure are in
millimeters. Determine pressures in the retort A, vessels B and C and
collector D.
390
255
185
140
Chapter 7 Solutions
System Dynamics
Ch. 7 - Prob. 7.1PCh. 7 - Refer to the water storage and supply system shown...Ch. 7 - Prob. 7.3PCh. 7 - In Figure P7.4 the piston of area A is connected...Ch. 7 - Refer to Figure 7.1.4a. and suppose that p\ — p2=...Ch. 7 - Pure water flows into a mixing tank of volume V =...Ch. 7 - Consider the mixing tank treated in Problem 7.6....Ch. 7 - Derive the expression for the fluid capacitance of...Ch. 7 - Prob. 7.9PCh. 7 - Prob. 7.10P
Ch. 7 - 7.11 Derive the expression for the capacitance of...Ch. 7 - Air flows in a certain cylindrical pipe 1 m long...Ch. 7 - Derive the expression for the linearized...Ch. 7 - Consider the cylindrical container treated in...Ch. 7 - A certain tank has a bottom area A = 20 m2. The...Ch. 7 - A certain tank has a circular bottom area A = 20...Ch. 7 - The water inflow rate to a certain tank was kept...Ch. 7 - Prob. 7.18PCh. 7 - Prob. 7.19PCh. 7 - In the liquid level system shown in Figure P7.20,...Ch. 7 - The water height in a certain tank was measured at...Ch. 7 - Derive the model for the system shown in Figure...Ch. 7 - (a) Develop a model of the two liquid heights in...Ch. 7 - Prob. 7.24PCh. 7 - Design a piston-type damper using an oil with a...Ch. 7 - Prob. 7.26PCh. 7 - 7.27 An electric motor is sometimes used to move...Ch. 7 - Prob. 7.28PCh. 7 - Prob. 7.29PCh. 7 - Figure P7.3O shows an example of a hydraulic...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - (a) Determine the capacitance of a spherical tank...Ch. 7 - Obtain the dynamic model of the liquid height It...Ch. 7 - Prob. 7.40PCh. 7 - Prob. 7.41PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - The copper shaft shown in Figure P7.46 consists of...Ch. 7 - A certain radiator wall is made of copper with a...Ch. 7 - A particular house wall consists of three layers...Ch. 7 - A certain wall section is composed of a 12 in. by...Ch. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - A steel tank filled with water has a volume of...Ch. 7 - Prob. 7.53PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.55P
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- The specific gravity of the 200ft^3 oil that weighs 10 520 lb isarrow_forwardQuestion 3 As part of a processing of biofuels, water is pumped into a circular tank with a diameter Dt, as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q₂. When the vessel is heated, water evaporates. The average velocity at which the vapour rises across the entire tank is vevap. You may assume that water has a density of pw, and vapour has a density of pv. Acceleration due to gravity is g. a) Find an expression for the rate of change of the mass of water in the tank. b) At time t = 0, the height of water in the tank is ho. Find an expression for the height as a function of time, h(t). c) An alarm is triggered when the pressure at the bottom of the tank exceeds Palarm. Find an expression for the time at which the alarm goes off. Q₁ V evap Dt Figure Q3: Water being pumped through a heated evaporation tank.arrow_forward2.14. A pump is driven by a two-speed motor having speeds of 1750 and 1185 rpm. At 1750 rpm, the flow is 45 gpm, the head is 90 ft, and the total efficiency is 0.60. The pump impeller has a diameter of 10 in. a. What values of Q, H, and ns are obtained if the pump runs at 1185 rpm? b. Find the specific speed and the specific diameter of the pump (at 1750 rpm).arrow_forward
- 1. Atmospheric pressure is about 80 kPa (absolute). Water pressure at the base of a water tower is 600 kPa (gauge). Determine the following: Gauge pressure at the base of the tower Absolute pressure at the base of the tower A pipe carries water at a flow rate of 90 L/s. Determine the minimum inside diameter so that the average velocity of the fluid does not exceed: 3 m/s 2 m/s 4 m/s A 20 mm diameter copper pipe (19.94 mm inside diameter) carries water at a flow rate of 40 L/s. Determine the average velocity of the fluid.arrow_forwardWater at 5°C is to be pumped from the river to the bottom of a water tower. The pump is 5 m above the river (dimension "a" on the diagram below) and is supplied by a 6.00 inch schedule 40 pipe. The tank is 19.5 m above the pump (dimension "b" on the diagram below) and is supplied by a 4 inch schedule 40 pipe. The water level in the tank is 4.3 m above the inlet (dimension "c" on the diagram below). The pump delivers 0.021 m/s. Losses are estimated to be 1.2 m between the river and the pump, and 4.2 m between the pump and the tank. Discharge line Suction line Pump River a) Calculate the losses in the suction line in kPa, based on the given head loss in m. kPa b) Calculate velocity in the suction line in m/s. m/s c) What is the pressure at the inlet to the pump in kPa? kPaarrow_forwardIn a continuous vertical cylindrical decanter, derive a formula to calculate the height, ZC, of the heavier liquid overflow leg. The pressure at the discharge point of the heavier liquid is given as 90% of the pressure on top of the fluid mixture. The heavier liquid's height is expressed as "ZB" and the lighter liquid's height as "ZA." The lighter liquid is denoted as "A," and the heavier liquid as "B." *Vapor pressure is not equal to atmospheric pressure.arrow_forward
- Example 4: If the diameter at section 1 is D₁ = 0.5 m, and at section 2 the diameter D₂ = 0.2 m. All the other conditions are the same as in Exercise #3. What power in kilowatts and in horsepower must be supplied to the flow by the pump? Assume h₁ = 3 m of water and a₁ = α₂ = 1. Water is being pumped through a system. D₁ = 0.5 m Z₁ = 30 m P₁ = 70 kPa gage α₁ = 1.0 1 Pump Sual Z₂ = 40 m P2 = 350 kPa gage %₂ = 1.0 D₂ = 0.2 m Head loss in pipe = 3 m Water Q = 0.5 m³/s Properties: Water (10°C, 1 atm, Table A.5): y = 9810 N/m³arrow_forward25.A tank contains 80 ft³ of air at a pressure of 350 psi. If the air is cooled until its pressure and temperature decrease to 200 psi and 70•F respectively, what is the decrease in internal energy?arrow_forward1. Water enters through a 23.616 inches diameter pipe under a pressure of 14 kPa. It leaves through a 900mm diameter exhaust pipe with a pressure of 4 kPa. A vertical distance of 8.2 ft separates the centers of the two pipes at the sections where the pressures are measured. If 500 liters of water pass the motor each second, compute the power supplied to the motor.arrow_forward
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