enter image description here

The rectangular gate will open authomatically, when the depth of water becomes very large. What is the minimum value of d that will cause the gate to just open? The width of the gate is 2 m.

  • $\begingroup$ This looks like homework or an exam / test question. Show what you have done so far. $\endgroup$
    – Solar Mike
    Apr 29, 2023 at 12:09
  • $\begingroup$ I used for a formula F= (specific weight x h x A). $\endgroup$ Apr 29, 2023 at 12:25

2 Answers 2


The hydrostatic pressure can be divided into constant part causing a force per width $\rho\cdot g\cdot h\cdot d$ plus linear part with force per width $\rho\cdot g\cdot \frac{h^2}{2}$, where $h=3m$ is the height of the gate. The constant part can be replaced by a force acting in the center of the gate, so with lever arm $L_1 = h/2-1.35$ above the hinge. The force from linear pressure part will act at the $h/3$ from the bottom, so with a lever arm $L_2 = 1.35-h/3$ below the hinge. When the resulting moment is zero, the moments on the hinge from both forces must be equal:

$$h\cdot d\cdot L_1 = \frac{h^2}{2}\cdot L_2$$

From that: $$d = \frac{h}{2}\frac{L_2}{L_1} = 3.5m$$


The hydrostatic pressureat any depth, as you said, is

$$p=\rho HA$$

  • H the depth measured from the bottom.
  • A is the width =2m

the total hydrostaic force apllied at H/3 is a triangular pressure diagram. $$F_h= \frac{H^2}{2} \rho A $$

the gate will open if the CG of hydrostatic force triangle falls above the hinge.

$$H/3> 1.2+1.35=2.55m$$ $$H\geq 3*255 \geq 7.65$$ $$d\geq (H -(1.20+3)) \geq 7.65-(1.2+3)\geq 3.45m$$

  • $\begingroup$ Aren't we going to use this equation (yp= yc + (Ixc/yc*A))? $\endgroup$ Apr 29, 2023 at 15:35
  • $\begingroup$ @AyçaArırt, the proof is in the pudding. why don't you plug in the d and see where the hydrostatic force acts? $\endgroup$
    – kamran
    Apr 29, 2023 at 17:19
  • $\begingroup$ Okey i gottcha. Thank u for helping. I appreciated. $\endgroup$ Apr 29, 2023 at 17:26
  • $\begingroup$ @AyçaArırt, please accept my answer then, so it helps other people looking for this kind of question. $\endgroup$
    – kamran
    Apr 29, 2023 at 17:34
  • $\begingroup$ I did it. Just one more question. Can I solve the this type of questions taking moment? $\endgroup$ Apr 29, 2023 at 18:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.