### Fluid Flow Between Lakes**(a)** Water flows by gravity from one lake to another, as illustrated. The surface levels of the lakes differ by an elevation of \( h = 50 \, \text{ft} \). If the volumetric flow rate is steady at \( Q = 80 \, \text{gallons per minute} \), what is the associated loss of available energy?**(b)** A pump is to be installed to pump the water from the lower lake to the upper lake with the same flow rate as above (\( Q = 80 \, \text{gallons per minute} \)). If the amount of energy loss is assumed to be the same as in part (a), how much mechanical power must be supplied by the pump?**Answer:**- **(a)** Loss = \( 1600 \, \text{ft} \cdot \text{lb/slug} \)- **(b)** \( \dot{W}_{\text{pump}} = 2.0 \, \text{hp} \)#### Diagram Explanation- **Illustration**: The diagram shows two bodies of water at different elevations, connected by a channel through which water flows. The height \( h \) between the lakes is marked at 50 feet. The channel likely represents the path of water flow due to gravitational pull.This problem demonstrates concepts of fluid mechanics and energy conservation, particularly in understanding how gravity and pumping power affect fluid flow between different elevations.

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Description: ### Fluid Flow Between Lakes**(a)** Water flows by gravity from one lake to another, as illustrated. The surface levels of the lakes differ by an elevation of \( h = 50 \, \text{ft} \). If the volumetric flow rate is steady at \( Q = 80 \, \text{gal

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(a) Water flows by gravity from one lake to another as illus- trated; the surface levels of the lakes differ by an eleva- tion of h= 50 ft. If the volumetric flow rate is steady at Q = 80 gallons per minute, what is the associated loss of available energy? (b) A pump is to be installed to pump the water from the lower lake to the upper lake with the same flow rate as above (Q = 80 gpm). If the amount of energy loss is assumed to be the same as in part (a), how much mechanical power must be supplied by the pump? Answer: (a) loss = 1600 ft-lb/slug, (b) Wpump = 2.0 hp

(a) Water flows by gravity from one lake to another as illus- trated; the surface levels of the lakes differ by an eleva- tion of h= 50 ft. If the volumetric flow rate is steady at Q = 80 gallons per minute, what is the associated loss of available energy? (b) A pump is to be installed to pump the water from the lower lake to the upper lake with the same flow rate as above (Q = 80 gpm). If the amount of energy loss is assumed to be the same as in part (a), how much mechanical power must be supplied by the pump? Answer: (a) loss = 1600 ft-lb/slug, (b) Wpump = 2.0 hp

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### Fluid Flow Between Lakes

**(a)** Water flows by gravity from one lake to another, as illustrated. The surface levels of the lakes differ by an elevation of \( h = 50 \, \text{ft} \). If the volumetric flow rate is steady at \( Q = 80 \, \text{gallons per minute} \), what is the associated loss of available energy?

**(b)** A pump is to be installed to pump the water from the lower lake to the upper lake with the same flow rate as above (\( Q = 80 \, \text{gallons per minute} \)). If the amount of energy loss is assumed to be the same as in part (a), how much mechanical power must be supplied by the pump?

**Answer:**

- **(a)** Loss = \( 1600 \, \text{ft} \cdot \text{lb/slug} \)
- **(b)** \( \dot{W}_{\text{pump}} = 2.0 \, \text{hp} \)

#### Diagram Explanation

- **Illustration**: The diagram shows two bodies of water at different elevations, connected by a channel through which water flows. The height \( h \) between the lakes is marked at 50 feet. The channel likely represents the path of water flow due to gravitational pull.

This problem demonstrates concepts of fluid mechanics and energy conservation, particularly in understanding how gravity and pumping power affect fluid flow between different elevations.

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