Application of Bernoulli Equation     

Example 2  (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 the datum for zero elevation and the streamline with point 1 at

the surface of the gasoline and point 2 where the salt water exits the nozzle of diameter, d.

 

Recall the data:  h = 2 ft,  e = 3.6 ft,  d = 0.06 ft  = diameter at nozzle exit from tank

Qo = 0.09 ft3/sec    γsalt water = 64.4 lb/ft3,   γgasoline = 42.5 lb/ft3. 

 

 

                                   

 

                    P1 + ½ ρV12 + γZ1  =   P2 + ½ ρV22 + γZ2 

 

At point 1:  V1 = 0 (large tank)     Since 2 fluids,  γZ1 = γgasoline h + γsaltwater e

At point 2:  P2 = 0 psfg,  Z2 = 0 ft,  V2 = Qo/A2  =  Qo / (πd2/4)  = 31.832 ft/sec

 

 P1  =    ½ ρ2V22   -  γgasoline h - γsaltwater e 

 

  P1 =  ½ (1.1)[(62.4)/32.2] (31.832)2 – 42.5(2) – (1.1)(62.4)(3.6)  =  748.9 psfg  =  5.2 psig

 

 

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