Oil flows in the s direction of the circular cross-section conduit shown below.

Question

Oil flows in the s direction of the circular cross-section conduit shown below. If the flow rate at any distance s or time t is 0.35 ft^3/s, is the flow classified as steady or unsteady; also uniform or nonuniform? In the system shown in the figure below, the value C is gradually closed so that the liquid volumetric flow rate steadily decreases over 4 s and is nearly but not completely closed from then on. How would you classify the flow with regard to steadiness and uniformly at A after 3 s? At B after 5 s?

Explanation / Answer

1) Flow is steady, as at any particular point velocity of fluid is constant because flow rate and cross section area is constant.{ flow rate = velocity*cross section area}

Flow is non-uniform because magnitude of velocity is changing from point to point.That is because cross section varies but flow rate is constant, hence, velocity will vary.

2) Again applying same concept as applied in question (1).

At point A, After 3 s valve is still getting closed, so flow rate must be changing hence the velocity at A. So, Flow is unsteady at A.

But At point B, we are talking after 5s when valve if not in motion. Flow is constant. Hence, Steady flow.

Here, In both the cases, cross section of the pipe is same throughout. Hence, at any particular instant of time. Velocity of fluid at any point near A and B is same. So, Flow is Uniform.

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