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Concept explainers
Under a number of simplifying assumptions, the steady state height of the water table in a one-dimensional, unconfined groundwater aquifer (Fig. P28.30) can be modeled with the following second-order ODE,
FIGURE P28.30
An unconfined or “phreatic” aquifer.
where
Solve for the height of the water table for
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Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The following table lists in order of magnitude the largest recorded discharge of a river with a drainage area of 12,560 km'. Year Q (m/s) 1948 2604 1933 2105 1928 1842 1932 1842 1917 1797 1947 1780 1921 1774 1927 1743 1938 1596 1936 1590 1922 1567 1912 1553 1925 1494 1924 1468 1916 1386 1918 1295 1292 1929 1943 1278 1919 1273 1323 1205 1939 1114 1934 1100 1945 1057 1935 1920 1046 1035 1914 995 1931 1913 1940 955 919 851 1942 851 1946 837 1926 817 1937 771 1944 769 1930 678 1941 618 1915 599 A. Estimate the 40- and 75-year inflow. B. What is the probability of the 100-year value occurring in any period of 7 consecutive year?arrow_forwardfluid 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_forward4 Discharge, Q through a venturimeter depends on the following variable Inlet pipe diameter - D Throat diameter - d Pressure drop across the venturimeter - Ap Fluid density - P Dynamic viscosity - µ Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenon 5 The droplet size, D produced by a liquid spray nozzle depends on the following variable Nozzle diameter - d Jet velocity - U Fluid density - p Dynamic viscosity – u Surface tension - o Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenonarrow_forward
- 7. An oil (sp.gr 0.9) is flowing through a 1.2m diameter pipe at a rate of 2.5 m³/s. The kinematic viscosity of oil is 3 X106 m²/s. In order to model this flow, water is used to flow through a 120mm diameter pipe having kinematic viscosity of 0.012X104 m²/s. Find the model discharge and velocity.arrow_forwardA graduated cylinder full of water in the lab on a bench that has just been waxed. The cylinder is 1 cm^2 in the inner cross-sectional area, and the water is 10 cm high. The temperature is at room temperature (25 °C) and remains constant. Water-air interface energy (i.e., water surface tension) is approximately 0.072 N/m at 25 °C. All the water spills and forms a puddle that can be approximated as a thin disk. (a) If this disk’s diameter is 14 cm, calculate the work required to create just the air-water interface. (b) Calculate the change in the gravitational potential energy of the water puddle in (b) (g = 9.8 m/s2arrow_forwardPROBLEM #1: Complete the data of the table below. Copy the entire table in your paper and use a different colored pen for your answers, you may also box your answers. Show solution. T:K P: kPa H: kJ/kg U: kJ/kg State (if wet steam provides xv as well) 1 525 350 2 125 2700 3 455.15 750 4 600 Xv = 0.8 5 200 1800 PROBLEM #2 A nozzle is used to increase the velocity of steam before it enters a turbine as a part of a power plant. The steam entering is at 1 MPa, 500 K and leaves at the conditions of 350°C and 2 MPa. If the nozzle has an inlet diameter of 3 cm and an outlet diameter of 1 cm, how much is transferred during the process? Is it lost or gained?arrow_forward
- The left and right water edges of a river are 2.75m and 62.45m, respectively, from an initial reference point. Verticals are located at distances 11.25, 19.25 26.75, 34.45, 40.95, 46.95, and 54.45 m, respectively from the reference point. The corresponding depths of verticals are 5.00, 9.60, 9.80, 10.00, 10.40, 10.00, and 4.80m. Mean velocities in the verticals are 0.16, 0.60, 0.75, 0.92, 0.97, 0.98, and 0.65 m/s respectively. A. Determine the Total Discharge of the river. B. Determine the average velocity of the river flow.arrow_forwardPROPAGATION OF ERROR You are tasked to supervise the design of 0.5MW wind turbine to be constructed in a Wind Farm in Pililla, Rizal. Suppose the design criteria are as follows: The air density as surveyed after 2 year period averaged at 1.225 kg / cubic meter. The sweeping diameter of the rotor blades is 125m, and the anemometer reading in the area amounts to 4.2m/s on a 2 year period of survey. What is the theoretical power output of the turbine assuming 100% efficiency of operation? Your answer must be in kW and in two decimal places with correct signs. In the previous problem, if the diameter measurement is off by 0.1m and the anemometer reading is also fluctuating by 0.05m/s and if the error measurement for theoretical power output must be limited to 3%, WHY OR WHY NOT should you accept the design? * Show complete solution in paper.arrow_forwardThe upward velocity of a rocket can be computed by the following formula: m. v = u ln mo gt qt where v =upward velocity,u = the velocity at which fuel is expelled relative to the rocket, m, = the initial mass of the rocket, q = the fuel consumption rate, and g = the downward acceleration of gravity (assumed constant =9.81 m/s2). %3D If u = 2200 m/s, m, = 160000 kg and q v = 1000 m/s using, = 2680 kg/s, compute the time at which 1. The graphical method, take t = 0 to 30 s with step (10 s). 2. The false-position method to within ɛ, = 0.12%. Use initial guesses of t = 20 s and 30 s. %3Darrow_forward
- What mathematical relationship exists between the wave speed and the density of the medium, using the POWER trendline equation from the graph? Make your response specific (i.e., describe the full mathematical proportionality between the two variables) Feel free to use the table. Table: Frequency (Hz) Density (kg/m) Tension (N) Speed (cm/s) Wavelength (cm) 0.85 0.1 4.0 632.5 744.12 0.85 0.7 4.0 239.0 281.18 0.85 1.3 4.0 175.4 206.35 0.85 1.9 4.0 145.1 170.70arrow_forwardFor a venturi meter given below, the volumetric flow rate is defined in terms of the geometrical parameters, the density of working fluid (p), and density of the manometer liquid (pm) as 4. Q = f(D, D2, A2, g, h, Pmv Pr) %3D Write down the balance equations and show your work to end up with an expression for the volumetric flow rate in terms of the variables defined above.arrow_forwardEXAMPLE Leaking Tank. Outflow of Water Through a Hole (Torricelli's Law) This is another prototype engineering problem that leads to an ODE. It concerns the outflow of water from a cylindrical tank with a hole at the bottom. You are asked to find the height of the water in the tank at any time if the tank has diameter 2 m, the hole has diameter 1 cm, and the initial height of the water when the hole is opened is 2.25 m. When will the tank be empty? 2.20 M Water level asime Outiine walls 200 200 30t .00- 50- D 10000 30000 tebe Revelion 50000arrow_forward
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