Calculating Acetone Pipe Network Flow Rates Correctly

The 1-inch branch flow changes when the 2-inch branch opens, even though the pump previously transferred about 100 gpm through the 3-inch line. Treat the reported flow and 40 psig discharge pressure as operating-point measurements, then solve the pump, common pipe, branch losses, valve positions, elevations, and 7 psig receiving-tank boundaries as one hydraulic network.

Required readings and boundary state

Before anything else, confirm the exact valve lineup and operating state to be calculated. A network solution applies to one defined state; opening or throttling either automated valve changes the system resistance and can move the pump to a different flow and discharge pressure.

1. Record whether the 1-inch and 2-inch automated valves are fully open, modulating, or at repeatable fixed positions. Obtain each control valve flow relation or operating Cv. A resistance coefficient for a fully open valve cannot represent a throttled valve.
2. Measure pump suction pressure and pump discharge pressure while both branches are in the target lineup. Record gauge locations and elevations. The reported 40 psig is useful only when its location and valve state match the case being solved.
3. Define the outlet boundary for each receiving tank. The tanks are maintained at 7 psig, but branch backpressure must also include elevation and, for a submerged connection, the liquid head above the entry point.
4. Confirm the common 3-inch pipe length of 100 ft, the 2-inch branch length of 39 ft, and the 1-inch branch length of 48 ft. Use actual inside diameters rather than nominal pipe sizes.
5. Inventory fittings, strainers, reducers, valves, and discharge connections by branch. Keep their loss coefficients assigned to the pipe velocity at the component location.
6. Obtain acetone viscosity at operating temperature and confirm that the stated density of 49 lb/ft³ applies to the transferred liquid. Density converts pressure to head; viscosity and roughness determine the friction factor.

Do not move on until every pressure is tied to a physical node and every elevation uses the same datum.

Pump-boundary decision

The first decision is whether the calculation must reproduce a measured snapshot or predict operation under other valve conditions.

A centrifugal pump normally supplies differential head as a function of total flow. It does not independently impose both 100 gpm and 40 psig. Adding parallel branches lowers or reshapes system resistance, so the intersection between the pump curve and system curve moves.

Do not calculate suction pressure by simply subtracting discharge pressure from total dynamic head. Apply the pump energy balance using consistent pressure, elevation, and velocity-head terms. Also keep suction pressure separate from the pump’s required net positive suction head: compare calculated available NPSH with the manufacturer’s required value at the solved flow.

Pipe and component loss functions

A friction-loss result cannot be correlated with flow unless it is expressed as a function of flow. For each uniform pipe segment, calculate velocity from V = Q/A and pipe-friction head from h_f = f(L/D)(V²/2g). Calculate fitting loss from h_m = ΣK(V²/2g). Determine the friction factor from Reynolds number, relative roughness, and the selected friction correlation.

Build three loss functions:

• R3(Q3) for the 100 ft, 3-inch common line from the pump discharge node to the split.
• R2(Q2) for the 39 ft, 2-inch branch from the split to its receiving-tank node.
• R1(Q1) for the 48 ft, 1-inch branch from the split to its receiving-tank node.

Each function must include pipe friction, its own fittings and strainer losses, control-valve pressure drop, and elevation change. Because velocity varies with diameter, do not add all fitting coefficients and apply one network-wide velocity.

Use 49 lb/ft³ only for pressure-to-head conversion after confirming the process condition. A pressure difference represents more feet of acetone head than the same pressure difference represents for water. Keep the complete calculation in either pressure or head units and convert once; mixing psi loss and feet of head without density conversion produces a false operating point.

Junction and outlet checks

The split imposes two non-negotiable network conditions: all connected pipes share one junction pressure, and flow is conserved at the junction. With no storage or third takeoff at the split, use Q3 = Q1 + Q2.

1. Calculate each effective outlet head from the 7 psig tank pressure, pipe-outlet elevation, tank liquid level when relevant, and the selected terminal-loss convention.
2. Guess a junction head Hj.
3. Solve Hj − Hout,1 = R1(Q1) for the 1-inch branch.
4. Solve Hj − Hout,2 = R2(Q2) for the 2-inch branch.
5. Add the branch flows to obtain Q3.
6. Calculate the 3-inch common-line loss at that total flow and determine the pump-discharge head required to support the guessed junction head.

Do not split the reported 100 gpm in proportion to nominal pipe area. Equal junction pressure does not create equal branch velocity or an area-based flow division. The 1-inch branch is longer than the 2-inch branch and has a smaller flow area; its valve, fittings, elevation, and outlet condition further determine its share.

Pump and system iteration

For a predictive calculation, close the network against the pump curve. At each trial total flow, obtain pump differential head from the curve, add it to the measured suction-side total head, and compare the resulting discharge head with the head required by the common pipe and both branches.

1. Choose a trial junction head and solve both branch flows.
2. Set common-pipe flow equal to their sum.
3. Calculate required pump discharge head from junction head plus R3(Q3).
4. Read available pump differential head at Q3 and combine it with suction total head.
5. If available discharge head exceeds required head, increase the trial flow or junction head. If it is lower, decrease the trial value.
6. Repeat until the pump balance, both branch balances, and Q3 = Q1 + Q2 close within the project’s calculation tolerance.

If a pressure controller holds the discharge at 40 psig, replace the uncontrolled pump boundary with the maintained pressure boundary and calculate the required control action. Then check the valve position or pump speed against its permitted operating range. A mathematical solution outside that range is not a realizable operating point.

Symptoms and deciding measurements

Resolving procedure and field verification

1. Place the system in the intended simultaneous-transfer state and wait for pump discharge pressure, tank pressures, and valve positions to stop drifting.
2. Record suction pressure, pump discharge pressure, junction pressure if a tapping exists, both 7 psig tank pressures, liquid levels, valve positions, and elevations.
3. Time the receiving-tank volume changes. Calculate each branch flow as Q = ΔVolume/ΔTime, using the tank calibration rather than raw level change when tank area varies with level.
4. Compare the measured branch flows with the hydraulic solution. Recalculate velocities separately as V1 = Q1/A1, V2 = Q2/A2, and V3 = (Q1 + Q2)/A3.
5. Use measured pressure drops to localize disagreement. A common-line mismatch points to the 3-inch model or pump boundary; a single-branch mismatch points to that branch’s valve, strainer, fittings, diameter, elevation, or outlet head.
6. Update only the input demonstrated by the measurement, solve again, and repeat the timed tank test with the same valve lineup.

Frequently asked questions