The watersupply network shown in Figure 1 has constanthead e

The water-supply network shown in Figure 1 has constant-head elevated storage tanks (reservoirs) at A and C, with inflow and outflow at B and D. The network is on at terrain with node elevations all equal to 30 feet. If all pipes are ductile iron with H-W roughness coefficient C_H = 100, compute the inflows/outflows to the storage tanks. Assume that flow in all pipes is fully turbulent. Step 1. Solve the problem using the Nodal method;

Solution

A0 without loss coeffs: the nodal eqns are first estimated.

Velocity of outflow from overhead tank is 56.17 ft/s

Q1= 56.17 *Area= 30.64

at first node: Qab-QAd= -30.64

at second node Qab +Qbc= 7.06

also 7.06 = Qad+Qcd

Qbc= Qcd+ Qout

solving we get Qout = 30.64 cft/s ( by mass continuity this must be saisfied)

Now apply friction factors

Head loss = KQⁿ n=2 ,K = 10.67/(C^1.85*d^4.87)

get K1= .0052, K2= .00213, K3= ,001, K4 =.00052

The head losses are introduced and new velocities, quatities computed. Iteration is reqd to converge to final value.