Question

The pressure, P (in lbs/ft2 ), in a pipe varies over time. Five times an hour, the pressure oscillates from a low of 90 to a high of 230 and then back to a low 90. The pressure at t = 0 is 90.

Question: Find a possible formula for P=f(t)

Answer 1

P=160-70*cos(2π*(1/12)*t)

• Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).

First, we find the amplitude by taking the difference between the peak values and dividing by two:

Amplitude=(230+90)/2=70

We can find the center value by either adding 70 to the minimum or subtracting 70 from the maximum:

90+70=160

230-70=160

This tells us that the Center Value=160

The frequency that we are operating at is given as:

f = 5/hour

so in minutes

f=5*(1/60)/minute=5/60=1/12 per minute

So, combining everything we get

P=160-70*cos(2π*(1/12)*t)

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