Inventory variations in a gas reservoir, a natural gas reservoir is to be supplied from a pipeline at a steady rate of go w 1 lb m hr During a 24 hour period, the fuel demand from the reservoir, w 2 , varies approximately as follows, w 2 A B cos wt where w t is a dimensionless time measured from th...

Inventory variations in a gas reservoir a The maximum minimum and average values of w are W min A B ...

Inventory variations in a gas reservoir, a natural gas reservoir is to be supplied from a pipeline

Question:

Inventory variations in a gas reservoir, a natural gas reservoir is to be supplied from a pipeline at a steady rate of go w₁ lb_m/hr. During a 24-hour period, the fuel demand from the reservoir, w₂, varies approximately as follows, w₂ = A + B cos wt where wt is a dimensionless time measured from the time of peak demand (approximately 6 A.M.)

(a) Determine the maximum, minimum, and average values of w₂ for a 24-hour period in terms of A and B.

(b) Determine the required value of w₁ in terms of A and B.

(c) Let m _tot = m⁰_totat t = 0, and integrate the unsteady mass balance with this initial condition to obtain into t as a function of time.

(d) If A = 5000lbm/hr, B = 2000lbm/hr, and p = 0.044lbm/ft³ in the reservoir, determine the absolute minimum reservoir capacity in cubic feet to meet the demand without interruption. At what time of day must the reservoir be full to permit such operation?