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- A Francis radial-flow hydroturbine has the following dimensions, where location 2 is the inlet and location 1 is the outlet: r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m. The runner blade angles are ?2 = 71.4° and ?1 = 15.3° at the turbine inlet and outlet, respectively. The runner rotates at n. = 160 rpm. The volume flow rate at design conditions is 80.0 m3/s. Irreversible losses are neglected in this preliminary analysis. Calculate the angle ?2 through which the wicket gates should turn the flow, where ?2 is measured from the radial direction at the runner inlet. Calculate the swirl angle ?1, where ?1 is measured from the radial direction at the runner outlet. Does this turbine have forward or reverse swirl? Predict the power output (MW) and required net head (m).The dimensions of a Francis radial-flow hydroturbine are r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m, where location 2 is the inlet and location 1 is the outlet. At the turbine inlet and outflow, the runner blade angles are β2 = 71.4° and β1 = 15.3°, respectively. The runner rotates at a rate of ń = 160 rpm. At design conditions, the volume flow rate is 80.0 m3 /s. (a) State the necessary assumptions and calculate the angle α2 at which the wicket gates should turn the flow (Figure Q1), with α2 measured from the radial direction at the runner inlet. (b) Calculate the swirl angle α1 (Figure Q1), where α1 is the angle measured from the radial direction at the runner output. (c) Calculate the needed net head and power output. (d) Discuss the actual power output and head required for actual case of the turbine (irreversibility not neglected). (Properties For water at 20oC, ρ = 998.0 kg/m3)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.
- The dimensions of a Francis radial-flow hydroturbine are r2 = 2.00 m, r1 = 1.30 m, b2 = 0.85 m, and b1 = 2.10 m, where location 2 is the inlet and location 1 is the outlet. At the turbine inlet and outflow, the runner blade angles are β2 = 71.4° and β1 = 15.3°, respectively. The runner rotates at a rate of ń = 160 rpm. At design conditions, the volume flow rate is 80.0 m3 /sAir fl ows through a variable-area duct. At section 1, A1 =20 cm2, p1 = 300 kPa, ρ1 = 1.75 kg/m3, and V1= 122.5 m/s.At section 2, the area is exactly the same, but the density ismuch lower: ρ2 = 0.266 kg/m3 and T2 = 281 K. There is notransfer of work or heat. Assume one-dimensional steady flow.(a) How can you reconcile these differences? (b) Find the massflow at section 2. Calculate (c) V2, (d ) p2, and (e) s2 - s1.[Hint: This problem requires the continuity equation.]Three immiscible fluiids are contained in a tank: 1.0 m of water, 1.20 m of oil (s= 0.80) and air under a pressure of 16 kPa. The tank is closed and has a height of 3.0 m and diameter of 1.0 m. Find the theoretical velocity throught a 5 cm diameter orifice located 30 cm above the bottom of the tank.include your free body diagrama.15.8 m/s b.10.34 m/s c.12.56 m/s d.8.03 m/s
- A Francis radial-flow hydroturbine has the following dimensions, where location 2 is the inlet and location 1 is the outlet: r2 = 6.60 ft, r1 = 4.40 ft, b2 = 2.60 ft, and b1 = 7.20 ft. The runner blade angles are ?2 = 82° and ?1 = 46° at the turbine inlet and outlet, respectively. The runner rotates at n. = 120 rpm. The volume flow rate at design conditions is 4.70 ×106 gpm. Irreversible losses are neglected in this preliminary analysis. Calculate the angle ?2 through which the wicket gates should turn the flow, where ?2 is measured from the radial direction at the runner inlet. Calculate the swirl angle ?1, where ?1 is measured from the radial direction at the runner outlet. Does this turbine have forward or reverse swirl? Predict the power output (hp) and required net head (ft).A dam is proposed on a remote stream that measures approximately 25-cm deep by 350-cm wide with an average velocity of 2.2 m/s. If the dam can be constructed so that the free surface above a turbine is 10 m, estimate the maximum power output of an 88 percent efficient turbine. a. 145kW b. 188kW c. 155kW d. 166kWConsider two identical wind turbines with a hub height of 40 m, one located in flat agricultural land and one located above a forest. What is the relative output power for the two turbines if the wind velocity is 10 m/s at a height of 100 m in both cases? Pagricultural/Pforest = ?
- Three immiscible fluiids are contained in a tank: 1.0 m of water, 1.20 m of oil (s= 0.80) and air under a pressure of 16 kPa. The tank is closed and has a height of 3.0 m and diameter of 1.0 m. Find the theoretical velocity throught a 5 cm diameter orifice located 30 cm above the bottom of the tank.CHOICES: a.10.34 m/s b.15.8 m/s c.12.56 m/s d.8.03 m/s35 - Water is drawn from the bottom of a large tank filled with water open to the atmosphere. If the outlet velocity is 4.6 m/s, what could be the height of the water in the tank? a) 2.24m B) 2.12m NS) 1.07m D) 1.60m TO) 4.33mThree immiscible fluiids are contained in a tank: 1.0 m of water, 1.20 m of oil (s= 0.80) and air under a pressure of 16 kPa. The tank is closed and has a height of 3.0 m and diameter of 1.0 m. Find the theoretical velocity throught a 5 cm diameter orifice located 30 cm above the bottom of the tank. a. 10.34 m/s b. 12.56 m/s c. 8.03 m/s d. 15.8 m/s With FBD