Hi everyone,

I am just having a little bit of trouble with the below calculation and was hoping that someone could help.
I can get an answer but not one of the ones below?

Two cylinders with pistons A & B are connected by a pipe containing water. The diameter of A is 125mm and B is 500mm and the face of the smaller piston is 6.0m above the larger. This is the DWT (Deadweight Tester) principle.

What force needs to be applied to the piston of cylinder A to maintain the load of 2,500Kg on the piston of cylinder B?

Tick ONE box:

a. 764 N
b. 764 Pa
c. 64 KN
d. 1528 N

 

Option "D" is the right answer.

Pascal's principle is defined as: A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid.

According to this principle, the pressure (because of the weight) applied at piston "B" will transmit to piston "A". In order to balance this pressure at piston "A" a counter pressure (force) must be applied.
<pre>Pressure at piston A= Force at piston A/Area of piston A
= Fa/(Pie*125^2)
Pressure at piston B= Force at piston B/Area of piston B
= Fb/(Pie*500^2)
= 2500*9.81/(Pie*500^2)</pre>
Now you can solve for Fa.

Hope this helps!

 

Option D is nearer to the value but not matching. Answer is 1532 N.

In the above reply<pre>
"Pressure at piston A= Force at piston A/Area of piston A
= Fa/(Pie*125^2)
Pressure at piston B= Force at piston B/Area of piston B
= Fb/(Pie*500^2)
= 2500*9.81/(Pie*500^2)"</pre>
In these diameters were used instead of radius but it did not effect the answer.

 

Both the previous answers are incorrect, and miss the point that "the face of the smaller piston is 6.0m above the larger". This head of water will develop its own pressure of rho.g.h = 1000 x 9.81 x 6 = 58.8 kN.

Yes - if you are using a deadweight tester, you need to include a correction for differences in elevation between the loaded piston and the gauge under test.

Note that you are given a mass for the applied load at B rather than an applied force - the load in N is then m x g.

So the pressure at the larger piston will be 58.8 kN with no load applied to the smaller piston.

The equation is then
Pressure at A = Pressure at B - rho.g.h
Force at A/ Area A = Force at B /Area B - rho.g.h

Force at A = ((mass at B x g)/Area B - rho.g.h) x Area at A

which gives 810 N -(not one of the given answers although the nearest is A. The actual value in force terms will depend on the figure used for "g", which will normally be within +-0.3% of the nominal 9.80665 m/s^2.

So my answer would be "none of the above - within the accepted industrial limits of accuracy".

 

Oops - the pressure due to the head is of course 58.8 kPa, not kN.