Equal Percentage characteristic can be identified by equal increments of X axis that yield equal percentage increments of the y-axis.

Whereas, in a linear characteristic, equal increments of x-axis yield equal increments in the y-axis.

Linear curve is simple as equation is just y=x.

I need help for the equation for equal percentage curve.
Either equation or how to generate it in excel will be gr8.

I have posted this picture of both linear(1) and equal percentage curve(2)  which will tell you what I am asking.
Thanks in advance

Any function f(x) that satisfy the equation f(x+a)= (1+a/100) f(x), where a is any fixed real number, has that property.

when x is 40%, i am not getting y=10%

That's not equal percentage then. for 40% increase in x, y should also increase by 40% for an equal percentage curve (as per my understanding).

I am guessing you are looking for modified parabolic or hyperbolic, where small increase in y leads to greater increase in x.

y=K.exp(mx)+c

I don't have access to Excel or Matlab right now to verify. Try to apply yourself. Try playing around with K to get the percentage change. I am guessing, it should be 1/4 in your case assuming m to be 40.

well, it is exponential curve. I now realise that I was trying to be specific to that plot with generalized data. Parbatya ( I know you), I will contact you later on to be more specific and clear my confusion. I know you can help me.

lootekukur, well, it is when opening is 40%, flow is 10% (in the plot in first post). The book I am going through says it is equal percent(not modified parabolic or hyperbolic), but I cannot deny that possibility too. I will try to use that. Thanks

That's not equal percentage then. for 40% increase in x, y should also increase by 40% for an equal percentage curve (as per my understanding).

Yeso bhayo bhane ta linear bhai go ni haina ra?

For linear function , y = x since the slope is 1 ,

Now, for exponential can't you do,

 y = Ar^x  

where A=10^b and r =10^m  (m and b are the slope and the intecept of the line). I tried to plot on the matlab before post anything here but I couldn't since another program is running in my machine.

The formula is y/100=K^(x/100-1). K can be any constant which will change the shape/rate of the curve. Here is a check with K=20.

Here is example for 10% increase.
x                 y            percentage increase
0                 5.00             25.89
10               6.75             25.89
20               9.10             25.89
30              12.28             25.89
40              16.57             25.89
50              22.36             25.89
60              30.17             25.89
70              40.71             25.89
80              54.93             25.89
90              74.11             25.89
100            100.00           25.89

Here is example for 15% increase.
x                 y            percentage increase
0                  5.0                   36.2
15                7.83                  36.2
30               12.28                  36.2
45               19.25                  36.2
60               30.17                  36.2
75               47.29                  36.2
90               74.11                  36.2

Use this equation for your particular problem of 'CONTROL VALVE CHARECTERSTIC'

Y = 0.02 * EXP(3.91X) 

EXP means Exponential

X and Y are in fraction, i.e. 0.1 means 10 %

And the result looks like

0.00	0.02
0.10	0.03
0.20	0.04
0.30	0.06
0.40	0.10
0.50	0.14
0.60	0.21
0.70	0.31
0.80	0.46
0.90	0.68
1.00	1.00

Hope it helps

 

Parbatya

Here is the graph for K=20. You can draw the graph in excel using the formula.

dyamn...

_x

For 40% opening, 10 % flow, K should be 46.42

v2001,

is y=10% when x=40% all that is needed? that might be sufficient to fit the curve (mathematically) but doesn't sound technically right to me. there must be other requirements. if not, it's a strange problem.

it took me a while to figure that when you said, x is 40%, that's a value not percentage change.
an equal percentage curve is such that for the increase of x by same amount (in number, not in %), y changes by equal percentage. that is nothing but an exponential curve.

y=exp(x)
 
for your case, the generic curve y=Kexp(nx) +C should work. it's just the matter of finding the right values for constants for your problem IMO.


khaobadi,
it's not 10% or 15% increase, but 10% or 15% open (valve that is, in this case). And your second example does not yield same percentage change in y (flow). That is not equal percentage.

Parbatya's example also doesn't entail equal percentage curve IMO (by definition) although he was able to yield y=10% for x=40%.

Wait till the evening when i have time, i will get this done if you are not able to solve it till then.

LooTe, as far as my understanding of the equal percentage valve it is the equal percentage increment of flow for a equal lift.

From http://www.boacalgary.com/artvalve.html

Equal Percentage Characteristic - In a valve having an equal percentage characteristic, like movements of the valve stem at any point of the flow range changes the existing flow an equal percentage regardless of the existing flow.

Example:

Suppose a valve stem has been lifted 30 percent of its total lift and the flow at this time is 3.9 gal/min. Now assume that the valve opens an additional 10 percent of its full travel and that the flow increases to 6.2 gal/ nun or a 60 percent increase. Next, suppose that the valve stem moves an additional 10 percent so that it is now 50 percent open. The flow now will be 10 gal/min or another 60 percent increase in flow.

CT,  prolly in some civil/mechanical engineering problem. i am guessing--- some dam/turbine problem. but i don't know for sure. i am just interested in the mathematical bit.

------
yes khaobadi. that is exactly what i am saying, equal percentage flow for equal increment in valve opening.

but that example gives '59.something' percentage change in the first case and '61. something' percentage change in the second. i am sure, there is ought to be some tolerance, but that's just a tad bit big IMO. I am not sure if its tolerable for this particular problem (mechanical/civil)

and your second example of your first post gives '36.6' percentage' initially and '56.something' later on.

parbatya's solution also gives range of percentage change -- from 33% to 60%

i am thinking, there are other requirements to this problem (for it to be complete so as to get a unique answer). else, there could be myriad solutions and values for the constants --none of them giving a perfect equal percentage solution.

or it could just be that he wanted to draw just a close-to-accurate graph and that's it.

let's hear more from v2001.

Chanaa dai,

Actually this type of equation applies to flow charecteristics in control valve (In Hydraulics). I think there are different types of valves based on the charecteristics as fast opening, linear, equal percentage etc(actually I also forgot all, polera khaaiyo) In this equation,

Y = 0.02 e ^ (3.91X)

X is opening i.e 0 for 'close' and 1 for 'fully open' while Y is percentage rate of flow i.e 1 means fluid flowing in full capacity.

But I think those type of curves apply everywhere (I dont know others).

And Loots,

I just found out the constants based upon your quation. You have the right equation and if you watch my datas, you can find equal %(almost 48%) increase (not increment) with the equal % increment( not increase), IMO.  

BTW, I dont know the mathematical defintition of this 'Equal percentage curve' as I said in my first post I just like to apply mathematics but never done correctly.

Parbatya

don't worry dude,professor zee is always here for u..here is one hard math problem i recently solved

parbatya,
you rounded them numbers so i got diff. percentages when i calculated them (on my head). comes out to be 47.85% to be precise (with calc :P) so yeah that's one solution that you came up with.. Also n=4.0236 is the precise value in your solution (not 3.91), that will yield y=0.1 for x=0.4
----------

just to generalize this (for V2001 or for anyone who might be interested):

y=K.exp(nx)

the given condition, y=0.1 when x=40% can have multiple solutions for K and n.

putting these values in the above eqn:

n=[log(0.1)-log(K)]/0.4 (where log is a natural logarithm)

so based on your K, n is determined. To make sure it's a positive exponential curve (for positive increment), K<=0.1. Also to get real solution (not complex), K>0.

Hence 0<K<=0.1
Also, more the K, less will be your change in flow percentage (y%). Depending upon your requirement, K can be chosen and that will give n.

Let me tell you guys why I needed it. I work for a valve manufacturer and these linear and equal percent curve are to be dealt daily. But I was always confused with this curve.
Yesterday I realized that I was trying to generalize a specific curve.
Anyway, thanks to all of u. I will try to get some detail about the valve profile curve including mathematics behind it and will share with you guys if they turned out to be interesting.

Solve this man

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