Bernoulli's principle: A level pipe contains a nonviscous, incompressible fluid with a density 1200 kg/m³ that is flowing steadily. At one position within the pipe, the pressure is 300 kPa and the speed of the flow is 20.0 m/s. At another position, the pressure is 200 kPa. What is the speed of the flow at this second position? A) 567 m/s B) 16.2 m/s C) 32.9 m/s D) 23.8 m/s E) 186 m/s

Question

Quizplus · Accepted Answer

According to Bernoulli's principle, the total energy (sum of kinetic energy, potential energy, and pressure energy) of a nonviscous, incompressible fluid is conserved along a streamline. Mathematically, this principle can be expressed as:

ρgh + 1/2 ρv^2 + P = constant

where ρ is the density of the fluid, g is the acceleration due to gravity, h is the height above a reference point, v is the speed of the flow, and P is the pressure of the fluid.

At the first position, we know that P = 300 kPa and v = 20.0 m/s. Let's assume that the height is the same at both positions (i.e. h1 = h2). Then we can write:

1/2 ρv1^2 + P1 = 1/2 ρv2^2 + P2

Substituting the given values, we get:

1/2 (1200 kg/m^3)(20.0 m/s)^2 + 300 kPa = 1/2 (1200 kg/m^3)v2^2 + 200 kPa

Simplifying this equation, we can solve for v2:

v2 = sqrt[(2(1/2 (1200 kg/m^3)(20.0 m/s)^2 + 300 kPa - 200 kPa))/1200 kg/m^3] = 23.8 m/s

Therefore, the answer is (D) 23.8 m/s.

Bernoulli's Principle: a Level Pipe Contains a Nonviscous, Incompressible Fluid