力学作业（英文版）- (11).pdf

Problem Set 2B Name: ____________________
Assigned: Thursday, September 13
Due: Tuesday, September 18



1. Complete the following statements:

a) If you took a long time-exposure photograph of a luminous particle moving with
the flow in a river, the image would be a ( pathline , streakline , streamline ).

b) A ___________________ is a curve in a flow field which has the property that
the velocity vector of each particle on the curve is tangent to the curve.

c) There are a ( finite , variable , infinite ) number of streamlines in a flow field.

v v
d) If dR is the infinitesimal displacement vector along a streamline and V is the
v v
velocity of a particle on the streamline, then dR ×V = ________ .

e) If you continuously inject dye at a fixed point into a flowing fluid in such a way
that the dye particles essentially match the speed of the fluid as they enter the
flow, the pattern of dye you see in a snapshot of the flow is a ( pathline ,
streakline , streamline ).

f) A streamline is an ( Eulerian , Lagrangian ) concept.

g) A pathline is an ( Eulerian , Lagrangian ) concept.


2. If you saw a plot of a flow in which two initially separate streamlines eventually
intersected with each other at a point, what would that necessarily tell you about the fluid
velocity at that point? Why?