Question

Figure OQ14.1 shows aerial views from directly above two dams. Both dams are equally wide (the vertical dimension in the diagram) and equally high (into the page in the diagram). The dam on the left holds back a very large lake, and the dam on the right holds back a narrow river. Which dam has to be built more strongly? (a) The dam on the left (b) The dam on the right (c) Both the same (d) Cannot be predicted

Short answer

The dam on the left has to be built more strongly, because height is more on left side and hence pressure will be more on left side. Therefore option (a) is correct.

Step-by-step solution

Pascal’s Law

The pressure in a fluid at rest varies with depth h in the fluid according to the expression

$p=p_0+\rho gh$

Where $p_0$is the pressure at $p$and$\rho$ is the density of the fluid, assumed uniform. Pascal’s law states that when pressure is applied to an enclosed fluid, the pressure is transmitted undiminished to every point in the fluid and to every point on the walls of the container.

Find which dam has to be built more strongly

Since $H_L>H_R$so, according to Pascal’s law pressure is more on left side. Also .area is more on left portion as,

$$\begin{gathered} Area=breath\times Height \\ \text{Left}\left(\text{Area}\right)=a.H_L>\text{Right}\left(\text{Area}\right)=b.H_R \end{gathered}$$

So, total force on left portion is more and hence left dam should be built more strongly.

Hence option (a) is the correct answer for this question.

Option [(a)The dam on the left] is correct.