Chapter 9.5, Problem 17FP

Water has a density of ρ = 1 Mg/m³.

Prob. F9-17

To determine

The magnitude of the hydrostatic force acting per meter length of the wall $\left(F_R\right)$.

Answer to Problem 17FP

The magnitude of the hydrostatic force acting per meter length of the wall $\left(F_R\right)$ is $\underset{\_}{\text{177}\text{kN}}$.

Explanation of Solution

Given:

The density of the water $\left({\rho }_w\right)$ is $\text{1}{\text{Mg/m}}^{\text{3}}$.

The height of wall $\left(h\right)$ is 6 m.

Explanation:

Determine the loading intensity $w_b$ of the wall.

$w_b={\rho }_{w}ghb$ (I)

Here, the acceleration due to gravity is g and the width of the wall is b.

Determine the magnitude of the hydrostatic force $F_R$ acting per meter length of the wall.

$F_R=\frac{1}{2}{w}_b\left(h\right)$ (II)

Conclusion:

Substitute $\text{1}{\text{Mg/m}}^{\text{3}}$ for ${\rho }_w$, $\text{9}\text{.81}{\text{m/s}}^{\text{2}}$ for g, 6 m for h, and 1 m for b in Equation (I).

$\begin{array}{c}{w}_b=\left(\text{1}{\text{Mg/m}}^{\text{3}}\right)\left(\text{9}\text{.81}{\text{m/s}}^{\text{2}}\right)\left(6\text{m}\right)1\\ =\left(\text{1}{\text{Mg/m}}^{\text{3}}\times 1,000\frac{\text{kg}/{\text{m}}^{\text{3}}}{{\text{Mg/m}}^{\text{3}}}\right)\left(\text{9}\text{.81}{\text{m/s}}^{\text{2}}\right)\left(6\text{m}\right)1\text{m}\\ =\text{58,860}\frac{\text{kg}}{{\text{m}}^{\text{3}}}\times \frac{\text{m}}{{\text{s}}^{\text{2}}}\times {\text{m}}^2\\ =\text{58,860}\frac{\text{kg}\cdot \text{m}}{{\text{s}}^{\text{2}}}\times \frac{\text{1}}{\text{m}}\times 1\frac{\text{N}}{\frac{\text{kg}\cdot \text{m}}{{\text{s}}^{\text{2}}}}\end{array}$

$=58.860\frac{\text{kN}}{\text{m}}$

Substitute $58.860\frac{\text{kN}}{\text{m}}$ for $w_b$ and 6 m for h in Equation (II).

$\begin{array}{c}{F}_R=\frac{1}{2}\left(58.860\frac{\text{kN}}{\text{m}}\right)\left(6\text{m}\right)\\ =177\text{kN}\end{array}$

Thus, the magnitude of the hydrostatic force acting per meter length of the wall $\left(F_R\right)$ is $\underset{\_}{\text{177}\text{kN}}$.