Question

A concrete gravity dam has 40 m height of water on its upstream side and 3 m water on its downstream side. If the level of water on the upstream side is increased by 1 m, the hydrostatic force acting on the dam will_____

• A. increase by 9.8 kN/m
• B. decrease by 9.8 kN/m
• C. increase by 4.9 kN/m
• D. decrease by 19.6 kN/m

Answer 1

The correct option is C increase by 4.9 kN/m

Case 1:
$h_1=\text{height of water on u/s side}=40m$
$h_2=\text{height of water on d/s side}=3m$

Hydrostatic force,
$F_{H1}=\frac{1}{2}{\gamma }_w{h}_1^2-\frac{1}{2}{\gamma }_w{h}_2^2$

Case 2:
$h_1^{\ast }=\text{height of water on u/s side}=41m$
$h_2=\text{height of water on d/s side}=3m$

Hydrostatic force,
$F_{H2}=\frac{1}{2}{\gamma }_w{h}_1^{\ast 2}-\frac{1}{2}{\gamma }_w{h}_2^2$

Change in hydrostatic force,

$=F_{H2}-F_{H1}$
$=\frac{1}{2}{\gamma }_w{h}_1^{\ast 2}-\frac{1}{2}{\gamma }_w{h}_1^2$
$=\frac{1}{2}\times 9.81\times (41-40{)}^2$
$=4.9kN/m$