We are evaluating when flow is steady, given a set of statements about flow behavior. Option a: 'flow velocity in a pipe is inversely proportional to flow area.' In a steady, incompressible flow, continuity implies that the volumetric flow rate Q is constant along a pipe, Q = A*v. Therefore, if the cross-sectional area A decreases, the velocity v must increase proportionally (v ∝ 1/A) to keep Q constant. This is a correct reflection of the steady-state continuity relationship. Option b: 'volumetric flow rate into a container equals volumetric flow rate out of the container, and the fluid is incompressible.' For a control volume enclosing the container, steady flow with no accumulation and incompressibility yields the condition Q_in = Q_out. Since the fluid is incompressible, density remains constant and volumetric flow rate can be used directly, making this a valid criterion for steady flow. Option c: 'a container is filled slowly.' A slow filling process does not guarantee that the flow is steady; it could be a transient condition with changing velocity, pressure, or accumulation inside the container. Steadiness requires that properties at a given location do not change with time, which slow filling alone does not ensure. Hence this statement is not a general guarantee of steady flow. Option d: 'mass flow rate into a container equals mass flow rate out of a container.' In steady-state situations with no accumulation, mass conservation demands that the mass flow rate in equals the mass flow rate out. This is a fundamental criterion for steady flow in a control volume, provided there is no storage of mass. Overall, options a, b, and d reflect core steady-flow (continuity) principles, while option c describes a process quality (slow filling) that does not by itself qualify as steady flow.

Flow is steady, when多项选择题

a. flow velocity in a pipe is inversely proportional to flow area.

b. volumetric flow rate into a container equals volumetric flow rate out of the container, and the fluid is incompressible.

c. a container is filled slowly.

d. mass flow rate into a container equals mass flow rate out of the container.

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Flow is steady, when多项选择题

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