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Fluid Dynamics

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Two problems on fluid dynamics:

Problem 1: Water flowing in a pipe with two sections with different cross section areas. To determine pressure, velocity and flow rates in the two sections.

Problem 2: Water in a tank being siphoned off. To determine velocity, pressure, flow rate etc..

See the attached file.

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Solution Preview

Please refer to the attachment.

1. a) Pressure at section 1 = Atmospheric pressure + Pressure due to the 3 ft water column

Pressure due to 3 ft water column (in psi) = Height of water column in inches x Density of water in pounds/cu.inch = 36 x 62.5/123 = 1.3 psi (Density of water = 62.5 lb/ft3)

As atmospheric pressure = 14.7 psi, p1 = 14.7 + 1.3 = 16 psi

b) Pressure at section 2 is atmospheric pressure as it is open to atmosphere.
Hence, p2 = 14.7 psi.

c) From continuity equation we have : a1v1 = a2v2 where a1 and a2 are the cross section area and v1 and v2 are the flow velocities at the two sections.

Or v2/v1 = a1/a2 = (Πx0.0752)/(Πx0.052) = 2.25 .......(1)

From Bernoulli's theorem we have : p1 + ½ d x v12 = p2 + ½ d x v22 (d = density of water)
(Note : As the pipe is horizontal, dgh terms on the two sides get cancelled out)

Or p1 - p2 ...

Solution Summary

Step-by-step solutions to the problems regarding fluid dynamics are provided.

See Also This Related BrainMass Solution

Fluid Dynamics Pressure Studies: Pressurized Tank Underwater

Please refer to two attachments for full details including diagram.

Phase 1

Valve A, B, and E are closed.
Tank A and B are separated and each sealed from the atmosphere.
Tank A initially has 3' of air @ 40 psi
Tank C and Tank B initially contain air @ 32.476 psi
Pipe K is 12" id; initial air pressure is 32.476 psi

Phase 2

Valve A, Valve B and Valve E are opened.
1. Will the combined pressure in Tank A push ALL the air in Tank C into Tank B?
2. If the answer for #1 is yes what changes take place in the following?
Valves A, B and E are closed when All air is pushed out from Tank C.
a. What changes take place in Tank C?
b. What changes take place in Tank B?
c. Are there any other notable changes from the original Phase 1?
d. What changes take place in Tank A?
1. What changes take place with the 3' of air @40psi?

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