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Water is to be pumped from a lake to a ranger station on the side of a mountain (see figure). The length of pipe immersed in the lake is negligible compared to the length from the lake surface to the discharge point. The flow rate is to be 95.0 gal/min, and the flow channel is a standard 1-inch. Schedule 40 steel pipe (ID = 1.049 inch). A pump capable of delivering 8 hp (= Ws ) is available. The friction loss F (ft-lbf /lbm) equals 0.0410 L, where L (ft) is the length of the pipe.

Water is to be pumped from a lake to a ranger station on the side of a mountain (see figure). The length of pipe immersed in the lake is negligible compared to the length from the lake surface to the discharge point. The flow rate is to be 95.0 gal/min, and the flow channel is a standard 1-inch. Schedule 40 steel pipe (ID = 1.049 inch). A pump capable of delivering 8 hp (= Ws ) is available. The friction loss F (ft-lbf /lbm) equals 0.0410 L, where L (ft) is the length of the pipe.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Water Pumping System from Lake to Ranger Station** Water is to be pumped from a lake to a ranger station on the side of a mountain. The length of pipe immersed in the lake is negligible compared to the length from the lake surface to the discharge point. The flow rate is to be 95.0 gallons per minute, and the flow channel is a standard 1-inch Schedule 40 steel pipe (ID = 1.049 inch). A pump capable of delivering 8 horsepower is available. **Friction Loss:** \[ \hat{F} \, \left(\text{ft} \cdot \text{lbf}_{f} / \text{lb}_{m}\right) = 0.0410 L, \] where \( L \) (feet) is the length of the pipe. **Diagram Explanation:** The diagram shows a simplified side view of the pumping system. The main components include: - **Lake:** The water source from which water is being pumped. - **Pipe:** A straight, inclined pipe represented by a black line. It transports water from the lake to the ranger station. - **Pump:** Illustrated as a circular device, it boosts water flow through the pipe. - **Incline Angle (\( \alpha^\circ \)):** The angle of the pipe relative to the horizontal ground. - **Length (L):** The full length of the pipe from the lake surface to the discharge point at the ranger station. - **Height (z):** The vertical distance between the lake surface and the discharge point. This setup illustrates the basic principles of fluid dynamics and hydraulic engineering used in designing efficient water transport systems on inclined terrains.
Transcribed Image Text:**Water Pumping System from Lake to Ranger Station** Water is to be pumped from a lake to a ranger station on the side of a mountain. The length of pipe immersed in the lake is negligible compared to the length from the lake surface to the discharge point. The flow rate is to be 95.0 gallons per minute, and the flow channel is a standard 1-inch Schedule 40 steel pipe (ID = 1.049 inch). A pump capable of delivering 8 horsepower is available. **Friction Loss:** \[ \hat{F} \, \left(\text{ft} \cdot \text{lbf}_{f} / \text{lb}_{m}\right) = 0.0410 L, \] where \( L \) (feet) is the length of the pipe. **Diagram Explanation:** The diagram shows a simplified side view of the pumping system. The main components include: - **Lake:** The water source from which water is being pumped. - **Pipe:** A straight, inclined pipe represented by a black line. It transports water from the lake to the ranger station. - **Pump:** Illustrated as a circular device, it boosts water flow through the pipe. - **Incline Angle (\( \alpha^\circ \)):** The angle of the pipe relative to the horizontal ground. - **Length (L):** The full length of the pipe from the lake surface to the discharge point at the ranger station. - **Height (z):** The vertical distance between the lake surface and the discharge point. This setup illustrates the basic principles of fluid dynamics and hydraulic engineering used in designing efficient water transport systems on inclined terrains.
Suppose the pipe inlet is immersed to a significantly greater depth below the surface of the lake, but it discharges at the elevation calculated in the previous part of the problem. The pressure at the pipe inlet would be greater than it was at the original immersion depth, which means that ΔP from inlet to outlet would be greater, which in turn suggests that more water could be pumped with the same power. In fact, however, less water can be pumped. Calculate the percentage decrease in flow rate caused by immersing the pipe inlet to a depth of 180 ft at the same angle (α = 40°).
Transcribed Image Text:Suppose the pipe inlet is immersed to a significantly greater depth below the surface of the lake, but it discharges at the elevation calculated in the previous part of the problem. The pressure at the pipe inlet would be greater than it was at the original immersion depth, which means that ΔP from inlet to outlet would be greater, which in turn suggests that more water could be pumped with the same power. In fact, however, less water can be pumped. Calculate the percentage decrease in flow rate caused by immersing the pipe inlet to a depth of 180 ft at the same angle (α = 40°).
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