Application of Bernoulli Equation     (continued)

 

Example 1  (continued)    Recall strategy for solution:

 

Step 1

Identify (draw) the streamline for application of the Bernoulli equation.

Step 2

Select the datum for the elevation, Z.  Identify points on the streamline and show known values of P, V, and Z.

Step 3

Write the Bernoulli equation between desired points.

Step 4

Solve for desired values.

 

The figure below shows steps 1 and 2 completed.

 

                       

 

  Step 3:     P1 + ˝ ρ V12 + γ Z1  =  P2  + ˝ ρ V22  +  γ Z2  ,        recall ρg = γ

 

The pressure gage measures “gage” pressure.  Note:  “gage” pressure is pressure

relative to atmospheric pressure.  So for point 1  on the streamline:

P1  =  10 psig  =  1440 lb/ft2 , Z1 = d =  5 ft, and for a “large” tank  V1 = 0 ft/sec. 

For point 2 on the streamline:  P2 = 0 psfg, V2  = 40 ft/sec, and Z2 = - e =  -10 ft.

 

1440 + 0 +  γ(5)  =  0 + ˝ (γ/g) 402 + γ(-10)   So  γ =146.27 lb/ft3

 

Now    specific gravity =  sg  =  γ/γwater  =   146.27/62.4  =  2.34     (result)

 

Click here for another example.

 

 

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