Problem 1.¶
For a given hypothetical flow, the velocity from time t=0 to t=5 seconds was u = 2m/s, v=0. Then from time t=5 seconds to t=10 seconds, the velocity was u= +3 m/s, v=-4m/s. A dye streak was started at a point in the flow field at time t=0, and the path of a particle in the fluid was also traced from that same point starting at the same time.
Draw to scale:
- the streakline
- path line of the particle, and
- streamlines at time t=10 seconds.
# list known quantities
# list unknown quantities
# governing principles
# solution (step-by-step)
# sketch here
# discussion
Problem 2.¶
Figure 1 is a schematic of a liquid flowing through a two-dimensional slot with a velocity of $V = 2\frac{q_0}{b}\frac{t}{t_0}$, where $q_0$ and $t_0$ are reference values.
What is the local acceleration at x = 2B and y = 0 in terms of B,$t$,$t_0$, and $q_0$?
# sketch here
# list known quantities
# list unknown quantities
# governing principles
# solution (step-by-step)
# discussion
Problem 3.¶
Water ($\rho = 1000 \frac{kg}{m^3}$) is accelerated from rest in a horizontal pipe that is 80 m long and 30 cm in diameter. If the acceleration rate (toward the downstream end) is 5 $\frac{m}{s^2}$, what is the pressure at the upstream end if the pressure at the downstream end is 90 kPa gage?
# list known quantities
# list unknown quantities
# governing principles
# solution (step-by-step)
# sketch here
# discussion
