At the darlington plant in Ontario, operators must know the rate of flow in the pipes cooling the reactors.However For operational and safety reasons, the pipes cannot be blocked by a measuring instrument. Instead, the pressure is measured before and after a narrowing of the pipe. The rate of flow is directly proportional to the square root of the difference in pressure deltaP where deltaP=P2-P1

a) Write the expression for rate of flow

b) The flow in pipe is 200 liters/min. If deltaP increases by 16%, what is the new flow rate?

Solution:

(a)

Delta P = P2-P1

The rate of flow: R

The proportion factor: k

So the experession of  rate of flow

R = k* sqrt(P2-P1)

(b)

R=200, P2-P1 = P, P'=1.16P, the new rate is R'

200 = k*sqrt(P)

R' = k*sqrt(1.16P)

R'= sqrt(1.16)*200 = 215.4

So the new rate of flow is 215.4 liters/min