Pressure to Achieve 10 m/s Flow Into Underwater Reservoir

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In summary, the question asks for the required pressure, Pr, to achieve a flow rate of 10 m/s into an underwater reservoir located 100 m below the surface. The fluid being transferred is liquid ammonia with a density of 682 kg/m^3 and the pipe diameter is 5 cm. In order to solve this, both Bernoulli's equation and the Darcy Weisbach equation must be used to account for the irreversible pressure drop in the pipe.
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Homework Statement


What pressure Pr, is required to achieve a flow rate of 10 m/s into the underwater reservoir if the tank is 100 m below the surface. Liquid ammonia is to be transferred with a density of 682 kg/m^3 and the pipe diameter is 5 cm. The reservoir underwater is at local hydrostatic pressure. A picture is included.

Homework Equations



Bernoulli's Eqn: P1 + (1/2)[tex]\rho[/tex]U2 +[tex]\rho[/tex]gz

The Attempt at a Solution


At first I thought that it was as simple as plugging in the values given into the formula and solving for P1, but then I realized that they gave us the diameter of the pipe too so I'm guessing it has some significance. I can't seem to figure it out though, any help would be great.

http://i429.photobucket.com/albums/qq12/ACE_99_photo/Untitled-2.jpg"
 
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  • #2
Hi Ace. Bernoulli's equation is just one of the necessary equations to calculate this. The other is the irreversible pressure drop of fluid that flows through a pipe which is best done using the Darcy Weisbach equation. You can plug the DW equation into the B equation simply by recognizing that there is a permenant pressure drop under flow equal to the pressure predicted by the DW equation.

Take a look at the DW equation and try to understand how the flow of fluid corresponds to some pressure drop in a pipe.
 

FAQ: Pressure to Achieve 10 m/s Flow Into Underwater Reservoir

1. What is "pressure to achieve 10 m/s flow into underwater reservoir"?

"Pressure to achieve 10 m/s flow into underwater reservoir" refers to the amount of force that is required to maintain a consistent flow rate of 10 meters per second into an underwater reservoir. This pressure is necessary to overcome the resistance of the water and ensure a steady flow of water into the reservoir.

2. Why is it important to achieve 10 m/s flow into underwater reservoirs?

Achieving a flow rate of 10 m/s into underwater reservoirs is important because it ensures a sufficient supply of water for various purposes such as irrigation, drinking, and industrial use. It also helps maintain the water quality and prevents stagnation, which can lead to the growth of harmful bacteria and algae.

3. How is the pressure to achieve 10 m/s flow into underwater reservoirs measured?

The pressure to achieve 10 m/s flow into underwater reservoirs can be measured using pressure gauges, which are typically installed at different points along the water pipeline. These gauges measure the force per unit area exerted by the water, and the readings can be used to adjust the flow rate to meet the desired pressure.

4. What factors can affect the pressure to achieve 10 m/s flow into underwater reservoirs?

The pressure to achieve 10 m/s flow into underwater reservoirs can be affected by several factors, including the elevation of the reservoir, the distance and diameter of the pipeline, the presence of any obstacles or bends in the pipeline, and the viscosity of the water. Other external factors such as temperature and changes in atmospheric pressure can also impact the pressure required for the desired flow rate.

5. Are there any techniques to improve the pressure to achieve 10 m/s flow into underwater reservoirs?

Yes, there are various techniques that can be used to improve the pressure to achieve 10 m/s flow into underwater reservoirs. These include using pumps to increase the pressure in the pipeline, installing pressure regulators to maintain a consistent pressure, and optimizing the pipeline design to reduce resistance and improve flow efficiency. Regular maintenance and cleaning of the pipeline can also help to maintain the desired pressure and flow rate.

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