Calculate weight of column of water know as head and piston force?

Question

I would like to build a water piston that will use water/gravity as force so I need to calculate the final net force on piston arm.

EXAMPLE: Piston head is 6.6 inches in diameter and stroke of 3 inches. A pipe 50 inches height x 0.5" inches Dia (total volume is 9.81 cubic inch) is connected to the cylinder inlet. Then with the help of gravity water is allowed in to the piston head causing it to go down due to the weight of water. So my questions are:

-I need a formula to calculate the weight or force of column of water pushing down inside the pipe in pounds

- Then with the resulting weight I need to calculate final force of the piston with the formula F= psi x Area., correct? Could you tell me the net force on the piston rod?

Hi There,
The column of water on pipe will not go empty. It contains water all the time.. Also, remember, I need the force on bottom of pipe but answers given were base in square inches, For example .433 psi per foot. Notice the bottom of pipe is half of a inch not an square inch.

I understand what you say and thank you for the comments. You right, I got the idea of psi all wrong that is why I need your help.
now I am getting more confuse when I think the following scenary. You state that 1.8 psi will remain the same regardles of pipe dia which is perfectly correct so help me understand this: A pipe with a dia of .00001" will produce same force on piston as a pipe 1" dia?. It drive me crazy thinking the idea that a pipe dia. has not effect on the piston net force output ? So again, if I use a pipe .00001" dia (or 1/4" as you mention) x 50" will give me 62lbs on the piston rod?

Answer 1

Using such a small diameter pipe, IF water will flow through it the effect will be the same but, wow! it will be slow.
The greater the diameter, the faster the pressure transfer.
(You should allow e-mails within 'Answers' profile, I could send a lot of answers regarding pressure and others).

A 1 foot head of water, regardless of volume or pipe size, will exert a static pressure of 0.433 psi.

(As proof of this, 1 ft³ of water = 62.4lbs.
The height of the cubic foot = 1foot.
The area of the base of the cube = 12 x 12 = 144in²
62.4lbs ÷ 144in² = 0.433 pounds/square inch (psi.)

1...Formula: Feet x 0.433 = Psi
So, your 50" pipe full of water = 4.2ft
4.2 x 0.433 = 1.8 psi.
(It will be the same for 50" of water in a 20,000gallon tank. But, the total force on the area of the tank base will be colossal.)

2.. F = 1.8 x Area = 1.8 x 3.142 x 3.3 x.3.3
....= 61.6 lbs force.

(Your piston area = 34.22in² with 1.8 lbs acting on each in² = 34.22 x 1.8 = 61.6 lbs ...this is not psi it's weight (force acting on the total area of the piston and if your pipe is maintained at 50", the water will run into the cylinder and fill it, it will produce a total force of 61.6lbs on the piston).

Edit: The actual diameter, volume or area of the pipe bottom has no bearing whatever on the pressure. Head (height) of water is the only unit needed to calculate water pressure.
If the area is 50 square inches, the pressure will still be 0.433 POUNDS on EACH SQUARE INCH.
Pressure is measured in Pounds PER Square INCH = PSI.
If the base area is only ¼ in², then the pressure of 1 foot of water wil be 0.433 ÷ 4 = 0.108pounds per ¼ in².
Pressure = Force ÷ Area. The unit used is PSI not ps¼i.

Let us say a storage tank with a base area of 5,000 in² contains 50" of water, it will exert a pressure of 1.8 pounds on EACH SQUARE INCH. (0.433 psi for each foot of height).
The TOTAL force acting on 5,000 in² = Pressure x Area = 1.8 x 5000 = 9,000 pounds. i.e. the mass of water in the tank.

Sorry to have to say this, but you all have the concept of pressure totally wrong.
....

Answer 2

1 psi = 2.31 ft of water
50 in / 12 in/ft = 4.167 ft
Pressure at pistion (psi)=height of water(ft)/2.31 ft/psi
Pressure at piston(psi)=4.167 ft / 2.31 ft/psi = 1.804 psi
Area of pipe = 3.14*.25in^2 =.19625 in^2
Force of column of water = 1.804 psi *0.19625 in^2 = 0.354 pounds force
1) Formula:
Pounds force of pipe(lbf) = Height(ft)/2.31 * 3.14 / 4 * pipe dia^2

2)The final pressure of the piston will be lower due to the volume of the piston cylinder. As the cylinder lowers to its 3 in stroke min. it will lower the over all height of the water column and the pressure it will delivery. The force will be the same due to the increase in area(F=psi*area) Both answers should equal each other.

Volume of cylinder(in^3)=3.14 / 4 * (6.6 in)^2 * 3 in = 102.63 in^3

This is more than the total volume of water in the pipe so the actual height in the piston cylinder is:

H(in) = 9.81 in^3 / 3.14 * 4 / (6.6in)^2 = 0.2869 inches = 0.0239 ft
So the force on the piston cylinder ends up to be:
Net Force(lbf)=0.0239ft / 2.31ft/psi * 3.14 / 4 * (6.6in)^2 = 0.354 lbf

Answer 3

The volume of the piston is 102.6 cu. inches.

The volume of liquid in your pipe is only 9.81 cu. inches, so you can only fill the cylinder with water to a depth of about 0.28 inches before the pipe is empty of water. This will probably not generate enough pressure to move the cylinder.

The maximum pressure on your cylinder with a head of 0.28" = 0.28/12 x 0.433 x 34.21 sq. in. = 0.35 lb force