Concept explainers
(a)
Volume flow rate between the two sections of the hose having a pressure difference
(a)
Answer to Problem 67PQ
The volume flow rate between the two sections of the hose having a pressure difference
Explanation of Solution
Bernoulli’s theorem states that the energy stored in the olive oil flowing through both narrow and wide part of hose is constant.
Apply Bernoulli’s theorem in the given situation.
Here,
Apply the continuity equation to find the relation between the velocities of oil in both parts of the hose.
Here,
Both wide and narrow parts of the hose are same height. Therefore,
Rewrite equation (I) to find
Here,
Write the equation to find the volume flow rate of the wide part of hose.
Here,
Write the equation to find the volume flow rate of the narrow part of hose.
Here,
Write the equation to find the area of the wide part of hose.
Here,
Write the equation to find the area of the narrow part of hose.
Here,
Write the equation to find the radius of wide part of hose.
Here,
Write the equation to find the radius of narrow part of hose.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Rearrange for
Substitute
Substitute
Therefore, the volume flow rate between the two sections of the hose having a pressure difference
(b)
Volume flow rate between the two sections of the hose having a pressure difference
(b)
Answer to Problem 67PQ
The volume flow rate between the two sections of the hose having a pressure difference
Explanation of Solution
Refer sub part (b).
Substitute
Substitute
Rearrange for
Substitute
Substitute
Conclusion:
Therefore, the volume flow rate between the two sections of the hose having a pressure difference
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