Final answer:
Using Bernoulli's equation, we can find the pressure difference between two segments of a horizontal pipe by arranging the equation as P2 - P1 = (1/2)ρ(v12 - v22) and substituting the given values for density and flow speeds.
Step-by-step explanation:
The question refers to the application of Bernoulli's equation to determine the difference in pressure (P2 - P1) between two segments of a horizontal pipe through which water flows. Bernoulli's principle states that for an incompressible, non-viscous fluid in steady flow, the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline.
To find the difference in pressure, we can use the following form of Bernoulli's equation:
P1 + (1/2)ρv12 = P2 + (1/2)ρv22
Where ρ is the density of the water, v1 and v2 are the flow speeds in the first and second segments of the pipe, and P1 and P2 are the pressures in the respective segments. Since the question does not provide values for P1 or P2, we cannot calculate their exact values but can arrange the equation to solve for the difference in pressure.
P2 - P1 = (1/2)ρ(v12 - v22)
Plugging in the given values:
P2 - P1 = (1/2)(1285 kg/m³((4.33 m/s)2 - (3.77 m/s)2)
The student can calculate the numerical value to find the pressure difference between segment one and segment two.