# Water Force - Static Fluid

1. Jun 19, 2017

### AutumnBeds

1. The problem statement, all variables and given/known data

A fresh water storage tank in a factory is shown in the figure above. Its top side is denoted as C, the narrow side as B and the long side as A. In order to allow regular maintenance and cleaning side A is hinged at its bottom edge and secured using a heavy-duty clasp at its top edge. L = 1.25m, H = 0.6m & W = 0.5m

Side a has a length of 1.25m and a height of 0.6m

(Assume the density of fresh water is 1000 kg/m3 and the acceleration due to gravity is 9.81 m/s2)

a) Draw a side on view of side A (looking along arrow D) and show the size of the two forces acting on the tank side and how high they are located from the bottom of the tank

2. Relevant equations

Resultant Force = Equilibrium Force in opposite direction

3. The attempt at a solution

I've calculated the water thrust force to be 2207.25 Newtons and it's height to be 0.4m meters from the top of the box.

I am correct in assuming that water thrust force is the resultant force? and the second force being the equilibrium force?

2. Jun 19, 2017

### haruspex

Including the water, I count three.
Check that.
A "resultant" force is the sum of a chosen set of forces. The sum of all the forces, in a static system, is zero. If you are choosing a subset, it depends which subset you choose.

3. Jun 19, 2017

### Staff: Mentor

Let's see your free body diagram.

4. Jun 19, 2017

### Staff: Mentor

I don't confirm your water total force magnitude, but I do confirm the location of its moment arm as 0.4 m from the top (0.2 m from the hinge).

5. Jun 20, 2017

### AutumnBeds

I've redone the workings, and hope this is somewhere along the lines of being correct.

I've based my workings on the following - http://physics.usask.ca/~chang/course/ep324/lecture/lecture8.pdf

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6. Jun 20, 2017

### Staff: Mentor

You have drawn a front view of the hinged door, not a side view (as requested in the problem statement). Please draw a side view of the hinged door, showing the force exerted by the hinge, the force exerted by the clasp, and the force exerted by the water on the door. Your calculation of F1 is correct, except that you forgot to multiply by g. I don't understand why you calculated F2, since that is not part of the problem (and I don't understand your derivation of F2). After you correct your calculation of F1, please calculate the moment of the force of the water about the hinge (please express it algebraically first).

7. Jun 20, 2017

### AutumnBeds

Hi Chester,

However, I am slightly confused. I had to ask the tutor who issued the work for clarity on the question;

Is this the forces acting on the wall and the base of the tank? YES

The way I read the question is that it is two forces acting on one side? YES - Water thrust on one side and then a force at each of the clasp and hinge on the other.

If I was to tale F2 again, and use it as the force acting against the centre of pressure on the door, would this be correct? and treat F3 as the force against the clasp (required force to keep door shut)?

Thanks,

8. Jun 20, 2017

### Staff: Mentor

His 2nd answer is correct. His first answer doesn't seem correct. You should only be looking at the forces acting on the door. I'm still waiting to see your correctly drawn diagram of the side view of the door, showing the forces of the water, clasp, and hinge.

9. Jun 20, 2017

### AutumnBeds

Hi Chester,

I believe that he is making reference to the final question which is to calculate the force required to keep the clasp shut;
a) Calculate the required resisting force at the clasp to keep the panel shut.

Amended work

10. Jun 20, 2017

### Staff: Mentor

This is the figure I had in mind:

At elevation z above the hinge, the water pressure is $$p=\rho g (h-z)$$
The differential pressure force on the section of door between z and z + dz is
$$dF=pwdz=\rho g w (h-z) dz$$where w is the width of the door (1.25 m).
The differential moment of pressure force (about the hinge) on the section of the door between z and z + dz is
$$dM=pwzdz=\rho g w(h-z)zdz$$
Please integrate these equations to get the total force F and the total moment M.

Last edited: Jun 20, 2017
11. Jun 21, 2017

### AutumnBeds

Hi Chester,

Thanks for the info. To be totally honest this all pretty much new to me and will take me a day to comprehend the above. I understand the basic formula, but when it's come to algebraic terms and integration I'm lost.

I've looked over my notes again and the only I can resolve which may be totally wrong is to calculate the water thrust on the opposite of the hinge and clasp and solve the resisting force on the clasp with F1D1=F2D2. F1 being the water thrust force and D1 the overturning moment from the hinge, D2 being the over all height of the door. The remaining force will on the hinge F3, and will be F1 - F2.

F2, Fclasp
F3, hinge

This may be the total wrong approach.

Your help so far is greatly appreciated.

12. Jun 21, 2017

### Staff: Mentor

This is actually very close to the way to do it.

If you integrate the water pressure distribution to get the water force F1, you get $$F_1=\rho g w\frac{h^2}{2}$$If you integrate the water pressure distribution to get the water moment M about the hinge, you get $$M=\rho g w \frac{h^3}{6}$$The distance you call D1 is the moment divided by the force: $$D_1=\frac{M}{F_1}=\frac{h}{3}$$Or, $$F_1D_1=M=\rho g w \frac{h^3}{6}$$So, now you have $$F_2D_2=\rho g w \frac{h^3}{6}$$
This gives you what you need to complete the solution (using the equations that you derived).

Chet

13. Jun 22, 2017

### AutumnBeds

Chet,

Both solutions return the same figures. I am confident I have submitted the work correct.

Thank you kindly for your assistance. It has been greatly appreciated.