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Chapter 12 | Fluid Dynamics and Its Biological and Medical Applications 507
Figure 12.9.)
Example 12.5 Calculating Pressure: A Fire Hose Nozzle
Fire hoses used in major structure fires have inside diameters of 6.40 cm. Suppose such a hose carries a flow of 40.0 L/s starting at a gauge pressure of . The hose goes 10.0 m up a ladder to a nozzle having an inside diameter of 3.00 cm. Assuming negligible resistance, what is the pressure in the nozzle?
Strategy
Here we must use Bernoulli's equation to solve for the pressure, since depth is not constant.
Solution
Bernoulli's equation states
where the subscripts 1 and 2 refer to the initial conditions at ground level and the final conditions inside the nozzle,
Similarly, we find
(This rather large speed is helpful in reaching the fire.) Now, taking to be zero, we solve Bernoulli's equation for :
(12.56)
Substituting known values yields
respectively. We must first find the speeds and . Since , we get
(12.53)
(12.54)
(12.55)
Discussion
(12.57)
This value is a gauge pressure, since the initial pressure was given as a gauge pressure. Thus the nozzle pressure equals atmospheric pressure, as it must because the water exits into the atmosphere without changes in its conditions.
Making Connections: Squirt Toy
Figure 12.10
A horizontally oriented squirt toy contains a 1.0-cm-diameter barrel for the water. A 2.2-N force on the plunger forces water down the barrel and into a 1.5-mm-diameter opening at the end of the squirt gun. In addition to the force pushing on the plunger, pressure from the atmosphere is also present at both ends of the gun, pushing the plunger in and also pushing the water back in to the narrow opening at the other end. Assuming that the water is moving very slowly in the barrel, with what speed does it emerge from the toy?
Solution
First, find the cross-sectional areas for each part of the toy. The wider part is
(12.58)
