Page 520 - College Physics For AP Courses
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508 Chapter 12 | Fluid Dynamics and Its Biological and Medical Applications
Next, we will find the area of the narrower part of the toy:
(12.59)
The pressure pushing on the barrel is equal to the sum of the pressure from the atmosphere ( )
and the pressure created by the 2.2-N force.
(12.60) (12.61)
The pressure pushing on the smaller end of the toy is simply the pressure from the atmosphere:
(12.62)
Since the gun is oriented horizontally ( ), we can ignore the potential energy term in Bernoulli's equation, so the equation becomes:
(12.63) The problem states that the water is moving very slowly in the barrel. That means we can make the approximation that
, which we will justify mathematically.
(12.64) (12.65)
(12.66)
How accurate is our assumption that the water velocity in the barrel is approximately zero? Check using the continuity
equation:
(12.67)
(12.68)
(12.69)
(12.70)
How does the kinetic energy per unit volume term for water in the barrel fit into Bernoulli's equation?
As you can see, the kinetic energy per unit volume term for water in the barrel is very small (14) compared to the other terms (which are all at least 1000 times larger). Another way to look at this is to consider the ratio of the two terms that represent kinetic energy per unit volume:
Remember that from the continuity equation
(12.71)
(12.72)
(12.73)
Thus, the ratio of the kinetic energy per unit volume terms depends on the fourth power of the ratio of the diameters:
This OpenStax book is available for free at http://cnx.org/content/col11844/1.14
