Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is 1.80 ✕ 105 Pa and the pipe radius is 2.50 cm. At the higher point located at y = 2.50 m, the pressure is 1.22 ✕ 105 Pa and the pipe radius is 1.30 cm.A pipe is open at both its left and right ends. The pipe starts at the left end, extends horizontally to the right, curves up and to the right, and extends horizontally to the right again. The right end is higher than its left end, and the change in height is labeled y. The diameter at the right end is smaller than the diameter at the left end. The pressure at the left end is labeled P1, and the pressure at the right end is labeled P2.(a) Find the speed of flow in the lower section. Your response differs from the correct answer by more than 100%. m/s(b) Find the speed of flow in the upper section. Your response differs from the correct answer by more than 10%. Double check your calculations. m/s(c) Find the volume flow rate through the pipe. Your response differs from the correct answer by more than 100%. m3/s

To solve this problem, we will use Bernoulli's equation, which states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant for an incompressible, non-viscous fluid in steady flow. The equation is:

P1 + 1/2ρv1² + ρgy1 = P2 + 1/2ρv2² + ρgy2

Given: P1 = 1.80 x 10^5 Pa r1 = 2.50 cm = 0.025 m P2 = 1.22 x 10^5 Pa r2 = 1.30 cm = 0.013 m y = 2.50 m ρ (density of water) = 1000 kg/m³ g = 9.81 m/s²

(a) To find the speed of flow in the lower section (v1), we first need to rearrange Bernoulli's equation to solve for v1. However, since the pipe is open at both ends, the fluid is exposed to atmospheric pressure at both ends, so P1 = P2. Also, since the lower section is our reference point, y1 = 0. Therefore, the equation simplifies to:

v1 = sqrt((2(P2 - P1) + 2ρgy2) / ρ)

Substituting the given values:

v1 = sqrt((2(1.22 x 10^5 - 1.80 x 10^5) + 210009.81*2.5) / 1000) v1 = sqrt((2(-5.8 x 10^4) + 4.9 x 10^4) / 1000) v1 = sqrt((-1.16 x 10^5 + 4.9 x 10^4) / 1000) v1 = sqrt(-7.1 x 10^4 / 1000) v1 = sqrt(-71)

Since the square root of a negative number is not a real number, there seems to be a mistake in the problem or in our calculations. The pressure at the lower point should be higher than the pressure at the higher point due to the effect of gravity.

(b) To find the speed of flow in the upper section (v2), we would use the continuity equation, which states that the volume flow rate is constant throughout the pipe. The equation is:

A1v1 = A2v2

However, since we were not able to find v1, we cannot find v2.

(c) To find the volume flow rate through the pipe, we would use the equation:

Q = A1v1 = A2v2

However, since we were not able to find v1 or v2, we cannot find Q.