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The growth of floating, unicellular algae below a sewage treatment plant discharge can be modeled with the following simultaneous ODEs:
where
where
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- Suppose that the population P(t) of a country satisfies the differential equation dP = kP(1200 – P) with k constant. Its population in 1960 was 300 million and was dt then growing at the rate of 2 million per year. Predict this country's population for the year 2010 This country's population in 2010 will be million. (Type an integer or decimal rounded to one decimal place as needed.)arrow_forwardA fire has been happened near a wall in a building, suppose the heat transfer f(x, y) = y²-K(x² + equation in the wall will be according to the equation: 2x - xy) a- Compute the constant (K) if you know that the heat transfer equation satisfy the following differential equation a²fa²f + = 0 дх2 т дуг b- Find the location of extreme heat value in the wall 4 2.arrow_forward3. The relationship between arterial blood flow and blood pressure in a single artery satisfies the following first-order differential equation: dP(t) + dt RC mmHg (cm³/s) P(t) = where Qin is the volumetric blood flow, R is the peripheral resistance, and C is arterial compliance (all constant). Qin-60 cm³/s and the initial arterial pressure is 6 mmHg. Also, assume R = 4 and C= 0.4- Oin cm³ mmHg (a) Find the transient solution Ptran(t) for the arterial pressure. The unit for P(t) is mmHg. (b) Determine the steady-state solution Pss(t) for the arterial pressure. (c) Determine the total solution P(t) assuming that the initial arterial pressure is 0.arrow_forward
- fluid mechanics A pipe 200 (mm) diameter carries Oil at a flow rate of 0.030 (m³/s). The pipe diameter reduces from 200 (mm) to 150 (mm). Point 1 is located at the beginning of the pipe and point 2 is located at the end of the pipe. Elevation of point 1 is 165 (m) lower than elevation of point 2. Water pressure at point 2 is atmospheric pressure. Water flow in the pipe ascending from point 1 to point 2. Total head losses of flow in the pipe equals to 15 (m). 1- Find the value of pressure head of Oil at point 1. 2- Draw the H.G.L. of flow in the pipe.arrow_forwardQ2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.arrow_forwardEnergy of a Roller Coaster Car 500 450 400 350 --- 3 300 250 E 200 150 100 50 6 8 10 Time (s) Mechanical Energy ....... Potential Energy -- Kinetic Energy This graph shows different types of energy for a roller coaster car that starts at the top of a large hill and goes down to its lowest point at 6 s. According to the graph, what is the most likely relationship between height and potential energy? Your answer: They are directly related. They are inversely related. There is no relationship between the two. There is not enough information for a conclusion.arrow_forward
- Kinetic energy of a fluid flow can be computed by 1 pv · vdV, where p(x, y, z) and v(x, y, z) are the pointwise fluid density and velocity, respectively. Fluid with uniform density flows in the domain bounded by x2 + z² = 6 and 0 < y<. = The velocity of parabolic flow in the given domain is v(x, y, z) 6 (6 – x² – 2²)j. Find the kinetic energy of the fluid flow.arrow_forward4:30 O M docs.google.com/forms/d/e 1.25 rad/s 5 rad/s 2.5 rad/s 20 rad/s 10 rad/s A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same wavelength, and same linear mass density, then the new power of the wave, is 500 W 125 W 1000 W 2000 W 250 W Page 2 of 2 IIarrow_forwardA closed thermodynamic system consists of a fixed amount of substance (i.e. mass) in which no substance can flow across the boundary, but energy can. For a closed themodynamic system we cannot add energy to the system, via substance (E ) (1.e. matter which contains energy is not allowed across the boundary) Across the Boundaries E° = No Q = = Yes W mass NO CLOSED = Yes SY STEM m = constant | energy YES Figure 1.1. If the substance inside the thermodynamic system shown in figure 1.1. (i.e. piston cylinder device) is air, is the system a Fixed closed system Moveable closed system A. В.arrow_forward
- The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground motion is represented by the following second-order linear ordinary differential equation: d?u dt2 du + c + ku = a, (t) m dt where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground acceleration. Suppose the building with a mass of 2000 kg and supported by columns of combined stiffness of 32 x 103 N/m is subjected to earthquake with ground acceleration given by the following function: ag(t) = 36000 cos 2t Find the equation of the displacement, u(t), given the damping is not installed to the building. Then, find how much the building is displaced from t =30 seconds to t =60 seconds of earthquake.arrow_forwardlail - Ahmed Amro Hussein Ali A x n Course: EN7919-Thermodynamic x Homework Problerns(First Law)_S x noodle/pluginfile.php/168549/mod_resource/content/1/Homework%20Problems%28First%20Law%29_SOLUTIONS.pdf UTIONS.pdf 4 / 4 100% Problem-4: When a system is taken from a state-a to a state-b, the figure along path a-c-b, 84 kJ of heat flow into the system, and the system does 32 kJ of work. (i) How much will the heat that flows into the system along the path a-d-b be, if the work done is 10.5 kJ? (Answer: 62.5 kJ) (ii) When the system is returned from b to a along the curved path, the work done on the system is 21 kJ. Does the system absorb or liberate heat, and how much? (Answer:-73 k]) (iii) If Ua = 0 andU, = 42kJ , find the heat absorbed in the processes ad and db. (Answer: 52.5 kJ, 10 kJ)arrow_forwardA higher-order differential equation given as y" + p(x)y' g (x)y = O is a homogenous equation, even if p(x) = 0. A higher-order differential equation given as y" + p(x)y' + q(x)y = 0 is also a homogenous equation, even if g(x) = 0. O Only first statement is true. O Only second statement is true. O Both first and second statements are true. O Both first and second statements are false.arrow_forward
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