Students’ conceptual difficulties in hydrodynamics

We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams complemented with several oral interviews, which were held with first-year engineering and science university students. Their responses allowed us to identify a series of misconceptions unreported in the literature so far. The study findings demonstrate that the most critical difficulties arise from the students’ inability to establish a link between the kinematics and dynamics of moving fluids, and from a lack of understanding regarding how different regions of a system interact.

Figure 1

Flow along a narrowing pipe. $P_1$ and $v_1$ ($P_2$ and $v_2$) indicate the pressure and the velocity before (after) the narrowing.

Figure 2

Fluid jet immersed in a still medium.

Figure 3

Container open to the atmosphere with pressure $P_0$ and two draining pipes. The dimensions and the places where the tracers are released are also indicated.

Figure 4

A fluid is flowing with different velocities in two horizontal pipes joined by an another vertical pipe.

Figure 5

Same setup as in Fig. 4 but in this situation two ends are blocked.

Figure 6

Open container with constant level $h$ discharging through a vertical pipe of length $L$.

Figure 7

Open container with a vertical draining pipe. Three points, 1, 2, and 3 at different heights $z_1$, $z_2$, and $z_3$, are indicated.

Figure 8

Two similar open containers, one of them with a vertical draining pipe of length $L$. The initial water level is $h$ in both containers.

Figure 9

Open container with water kept at a constant level $h$. The fluid drains through a pipe which ends with a vertical section of length $L$. Four points, $A$, $B$, $C$, and $D$ are represented, two inside the pipe and the other two after the mouth of the pipe.

Figure 10

Magnification of Fig. 9 in which two elements of the fluid with length $dy$ were represented.

Figure 11

Streamlines of a fluid moving in a vertical direction which encounters an obstacle (not represented here).