Mechanical Engineering - Hydraulics and Fluid Mechanics - Discussion

One-dimensional flow.

All the flow parameters may be expressed as functions of time and one space coordinate only.

The single space coordinate is usually the distance measured along the centre-line (not necessarily straight) in which the fluid is flowing.

Example: the flow in a pipe is considered one-dimensional when variations of pressure and velocity occur along the length of the pipe, but any variation over the cross-section is assumed negligible.

In reality, flow is never one-dimensional because viscosity causes the velocity to decrease to zero at the solid boundaries.

If however, the non-uniformity of the actual flow is not too great, valuable results may often be obtained from a "one-dimensional analysis".

The average values of the flow parameters at any given section (perpendicular to the flow) are assumed to be applied to the entire flow at that section.

I agree @Aman.

The one-dimensional flow does not necessarily mean a straight line.

Suppose an ant is moving in a zig-zag path. If we look at the path of an ant from above we will observe ant is moving in a zig-zag path which is lying on a 2d plane but if you ask the ant what is the path of your motion? The ant will definitely say that I am is moving in a straight line. Because ant will not be able to observe its motion from above. As soon as the ant takes turns on its path its X coordinate will also take a turn with it (ant). So if you are moving in a zig-zag path you can not say that you are moving in 2d. It will be ond D only.

Both B & D are correct as if the flow is one dimensional it will flow in a straight line. As one dimension always represents a single coordinate, i.e., U=f(x) if we consider flow along the x direction. But this explanation follows option D too as if the flow is considered along line x=y then with respect to the coordinate system which is tilted by 45 degrees it is a flow along the axis and hence again in a straight line.

So the velocity will be given as U=f(x') where x' would be the x direction in transformed axis and hence flow in a single direction is also a one-dimensional flow.

The single space coordinate is usually the distance measured along the center-line (not necessarily straight) in which the fluid is flowing.

Example: The flow in a pipe is considered one-dimensional when variations of pressure and velocity occur along the length of the pipe, but any variation over the cross-section is assumed negligible.

In reality, flow is never one-dimensional because viscosity causes the velocity to decrease to zero at the solid boundaries.

If pressure and velocity vary in one dimensional flow then pv remained constant as it graph shows. The straight line from origin. Usually fluid flowing in a pipe considered one dimensional flow. I hope it's something which make you understand.

For one dimensional flow, the velocity is the function of single coordinate (i.e) u= f(x).

Let u be the velocity.

The function u = f(x) is the straight line.

Therefore one dimensional flow is the straight line flow.

No, the One-dimensional flow has nothing to do with the straight line or curve. If the entire flow parameter requires only 1 independent variable to completely specify the flow then it is called one dimensional.

@Zxcv, here the question asked from kinematics.

So we can't consider the forces acting on it.

BUT you consider sheer force. So it is wrong.

And your explanation is correct to incase of dynamics.

Dear @Arun you are wrong.

One dimension does not mean like only in one space coordinates direction(as you say in x).

The direction may change from x to y coordinate direction but it is single.

Proper answer is D because if we think as straight line by considering u=f(x), it may have two components with respect to a reference point it means it represent 2d flow. So answer is D.