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FLUID MECHANICS - CASE STUDY SOLUTION


Problem Description

 

 


Forces on the Control Volume

 

First select a control volume to include the hose, nozzle and water inside the hose, as shown by the red dashed lines in the figure. Rx and Ry represent the reaction force components acting on the hose. W is the weight of the water inside the hose.

The linear momentum equation for steady flow is given by

                                       

which can be written in terms of x- and y- component as follows:

    x-component:
    p1A1 - p2A2cos45o + Rx
                      = V1ρ(-V1)A1 + V2cos45oρ(V2)A2

    y-component:
    - p2A2sin45o - W + Ry = V2sin45oρ(V2)A2

The gage pressure at the nozzle outlet is zero (i.e., p2 = 0) since water is discharged to the atmosphere. According to the principle of conservation of mass,

     

The linear momentum equations can be simplified to yield the reaction force in the x- direction:

    

     


Required Resultant Force for
Holding the Hose in Place

 

and the reaction force in the y-direction:

     

Hence, the resultant force required to hold the hose in place is given by F = 1.05i + 26.4j lb.     

     
   
 
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