A level pipe contains a nonviscous,incompressible fluid with a density 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

A level pipe contains a nonviscous,incompressible fluid with a density  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

Quizplus · Accepted Answer

From Bernoulli's equation, we know that:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

Where P1 and v1 are the pressure and speed at the first position, and P2 and v2 are the pressure and speed at the second position.

Plugging in the given values, we get:

300 kPa + (1/2)(11ea83ea_69e8_c664_aeff_dd99722dabcf_TB6394_11)(20.0 m/s)^2 = 200 kPa + (1/2)(11ea83ea_69e8_c664_aeff_dd99722dabcf_TB6394_11)(v2)^2

Simplifying this equation gives:

v2 = sqrt[(2/11ea83ea_69e8_c664_aeff_dd99722dabcf_TB6394_11)(300 kPa - 200 kPa) + (20.0 m/s)^2] = 23.8 m/s

Therefore, choice D is correct.

A Level Pipe Contains a Nonviscous,incompressible Fluid with a Density