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7.40. A cylindrical tank, shown in Fig. 7.29, is sitting on a platform with absolutely frictionless wheels on a horizontal plane. There is no air resistance. At time 0, the level in the tank is 10 ft above the outlet, and the whole system is not moving. Then the outlet is opened, and the system is allowed to accelerate to the left. The flow through the outlet nozzle is frictionless. What is the final velocity, assuming that (a) the mass of the tank and cart is zero and (b) the mass of the tank and cart is 3000 lbm? -10 ft 10 ft Exit area ft² FIGURE 7.29

7.40. A cylindrical tank, shown in Fig. 7.29, is sitting on a platform with absolutely frictionless wheels on a horizontal plane. There is no air resistance. At time 0, the level in the tank is 10 ft above the outlet, and the whole system is not moving. Then the outlet is opened, and the system is allowed to accelerate to the left. The flow through the outlet nozzle is frictionless. What is the final velocity, assuming that (a) the mass of the tank and cart is zero and (b) the mass of the tank and cart is 3000 lbm? -10 ft 10 ft Exit area ft² FIGURE 7.29

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**Transcription for Educational Website:** --- **Problem 7.40 Explanation** A cylindrical tank, depicted in Figure 7.29, is positioned on a platform with completely frictionless wheels on a horizontal surface, ensuring no resistance impedes movement. Initially, at time \( t = 0 \), the liquid level inside the tank is 10 feet above the outlet, and the system remains stationary. Once the outlet is opened, the system begins to accelerate to the left due to the exiting fluid. The flow through the outlet nozzle is considered frictionless. **Objective:** Determine the final velocity of the system under two conditions: 1. The mass of the tank and cart is zero. 2. The combined mass of the tank and cart is 3000 lbm. **Diagram Analysis (Figure 7.29):** - The tank has a height of 10 feet and sits on a cart with frictionless wheels. - The exit area for the liquid is specified as 1 square foot. - No external forces (e.g., air resistance) act on the system, allowing analysis based solely on internal fluid dynamics and momentum conservation. This setup is crucial for understanding fundamental principles of fluid dynamics and momentum conservation in a frictionless environment.
Transcribed Image Text:**Transcription for Educational Website:** --- **Problem 7.40 Explanation** A cylindrical tank, depicted in Figure 7.29, is positioned on a platform with completely frictionless wheels on a horizontal surface, ensuring no resistance impedes movement. Initially, at time \( t = 0 \), the liquid level inside the tank is 10 feet above the outlet, and the system remains stationary. Once the outlet is opened, the system begins to accelerate to the left due to the exiting fluid. The flow through the outlet nozzle is considered frictionless. **Objective:** Determine the final velocity of the system under two conditions: 1. The mass of the tank and cart is zero. 2. The combined mass of the tank and cart is 3000 lbm. **Diagram Analysis (Figure 7.29):** - The tank has a height of 10 feet and sits on a cart with frictionless wheels. - The exit area for the liquid is specified as 1 square foot. - No external forces (e.g., air resistance) act on the system, allowing analysis based solely on internal fluid dynamics and momentum conservation. This setup is crucial for understanding fundamental principles of fluid dynamics and momentum conservation in a frictionless environment.
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