流力期中考古題-2
1. Please explain the following terms:
(1) Streamline; (2) Pathline; (3) Streakline

x 
y 
i
j , please find the
2. An idealized velocity distribution is given by V 
1 t
1  2t
equations of (a) the streamline and (b) the pathline which pass through the point
(x0, y0) at the time t=0.
3. Please determine the rate at which the water level rises (or falls) in an open
container if the water coming in through a 0.10-m2 pipe has a velocity of 0.5 m/s
and the flow rate going out is 0.2 m3/s, as shown in Fig. 1. The container has a
circular cross section with a diameter of 0.5 m.
Fig. 1
4. For laminar flow in the entrance to a round pipe with the radius of r0, as shown in
Fig. 2, the entrance flow is uniform, u=U0, and the flow downstream at location x is
parabolic in profile, u (r )  C (r02  r 2 ) . Assume the pressure distribution at
location 0 is P0 and at location x is Px. P0 and Px are constant. At steady state, please
determine
(a) the value of C.
(b) the viscous drag force exerted on the pipe walls between 0 and x.
(c) Consider the heat-transfer aspect by assuming a uniform entrance profile
T=T0 and an exit profile approximated by T (r )  T0 (1.5  0.5r 2 / r02 ) . For
flow with constant properties and negligible kinetic and potential energy
changes, use RTT to calculate the total heat transfer rate (dQ/dt) through the
pipe walls between entrance and exit.
Fig. 2
5. Water is added to the tank shown in Fig. 3 through a vertical pipe to maintain a
constant (water) level. The tank is placed on a horizontal plane, which has a
frictionless surface. Determine the horizontal force, F, required to hold the tank
stationary. Neglect all losses. (Note: water density= 999 kg/m3)
Fig. 3
Fig. 4
6. Water is flowing steadily through the 180o elbow shown in Fig. 4. At the inlet to
the elbow the absolute pressure is 203 kPa. The water discharges to atmospheric
pressure (Pa= 100 kPa). Assume properties are uniform over the inlet and outlet
areas; A1= 2500 mm2, A2= 650 mm2, and V1= 3.0 m/s. Find the horizontal
component force required to hold the elbow in place. Neglect the elbow and water
weight. Also, neglect the pipe friction. (Note: water density= 999 kg/m3)
7. As shown in Fig. 5, a tank of fixed volume contains brine with initial density, ρi ,
greater than water. Pure water enters the tank steadily and mixes thoroughly with
the brine in the tank. The liquid level in the tank remains constant. Derive
expressions for (a) the rate of change of density of the liquid mixture in the tank,
and (b) the time required for the density to reach the value ρf , where
i   f   H 2 O .
Fig. 5
8. The velocity distribution of downstream of a 10-m-long circular cylinder is as
shown in Fig. 6. Determine the force of the air on the cylinder. The density of air
is 1.23 kg/m3.
Fig. 6