Consider the following statements about fluid flow. (Select T-True, F-False, G-G
ID: 1509004 • Letter: C
Question
Consider the following statements about fluid flow. (Select T-True, F-False, G-Greater than, L-Less than, E-Equal to. If the first is T the second F and the rest G, enter TFGGGG).
A) Bernoulli's equation is a statement of conservation of energy.
B) Bernoulli's equation applies to viscous fluids.
C) Streamlines sometimes cross each other.
D) As fluid flows through a pipe the pressure at a narrow point is ... the pressure where the pipe is wider.
E) If the radius of a water pipe becomes twice as large the flow speed of a non viscous fluid will be .... one fourth of its initial value.
F) Bernoulli's equation applies to compressible fluids.
Explanation / Answer
Answer: T F F L G F
Part A:
-Bernoulli's equation is a statement of conservation of energy.
TRUE Bernoulli's equation is specifically at statement of conservation of energy ALONG A STREAMLINE.
Part B:
-Bernoulli's equation applies to viscous fluids.
FALSE.
Part C:
Streamlines sometimes cross each other.
FALSE, the velocity is everywhere tangent to a streamline. So if a streamline intersects itself, then the velocity must be multi-valued at the point of intersection.
Part D:
- As fluid flows through a horizontal pipe the pressure at a narrow point is "less than" the pressure where the pipe is wider .
it depends on the flow regime involved.
in the incompressible flow situation, the static pressure is lowest at the point of maximum velocity -- so "less than" is the right phrase to use.
Part E:
-If the radius of a water pipe becomes twice as large, the flow speed of a non viscous fluid will be "greater than" one fourth of its initial value.
it depends.
if the water completely fills the entire pipe, then continuity says the flow speed should equal 1/4 the initial flow speed.
however, consider the situation where the pipe diameter is huge (2 people high) but is mostly filled with air -- the water flow is but a trickle along the bottom of the pipe. in that case, when the pipe radius increases, the flow speed will not change very much because the cross-sectional area that the water is flowing through doesn't change very much (that cross-sectional area being vastly different from the cross-sectional area of the pipe!) -- so the trickle remains a trickle. In that limiting case, the flow speed is approximately equal to the initial flow speed.
So since 1 > 1/4, the best you can say is "greater than", given the problem parameters and lack of specificity.
Part F:
-Bernoulli's equation applies to compressible fluids.
FALSE - Bernoulli's equation is a statement about conservation of energy along a streamline. The classical Bernoulli relation only balances static pressure (potential energy) and dynamic pressure (kinetic energy) there is no compressibility term -- work done to effect density changes would be reflected by an additional term involving an equation of state. That term is not present in what is the classical Bernoulli relation.