---
title: "Three reservoirs ZA 65, ZB 70, ZC 40"
subject: "Hydraulics"
chapter: 3
key: "semester_4/hydraulics:three-reservoir-pipes-ad-bd-dc"
source: https://www.bctengineer.com/q/semester_4/hydraulics/three-reservoir-pipes-ad-bd-dc
site: BCT Engineering
---

# Three reservoirs ZA 65, ZB 70, ZC 40

Hydraulics · Chapter 3: Three reservoirs problem and Pipe networks

- Asked in: 2073 Magh, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/three-reservoir-pipes-ad-bd-dc
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-3

## Question

In the reservoir system of figure $Z_A$ = 65 m, $Z_C$ = 40 m, $Z_B$ = 70 m, BD = 900 m of 10 cm diameter pipe, AD = 600 m of 2.5 cm diameter pipe and DC = 150 m of 15 cm diameter pipe. Using f = 0.025 and neglecting minor losses, determine the flow in each pipe. [Figure: reservoir A (65 m) and reservoir B (70 m) joined at junction D; pipe DC leads to outlet C at 40 m discharging to atmosphere; horizontal datum below]

## Short answer

With resistance factors computed from pipe lengths, diameters and f = 0.025, trial HJ is adjusted to satisfy continuity at junction D. At HJ = 40.69 m, the flows are: Q_AD = 0.44 L/s (A→D), Q_BD = 12.56 L/s (B→D), Q_DC = 12.99 L/s (D→C), all from higher to lower head.

## Answer

**Data.** $Z_A = 65$ m, $Z_B = 70$ m, $Z_C = 40$ m; AD: 600 m, 25 mm; BD: 900 m, 100 mm; DC: 150 m, 150 mm; $f = 0.025$. Only friction, $h_f = rQ^2$, $r = \dfrac{8fL}{\pi^2gD^5}$.

| Pipe | L (m) | D (m) | r (s²/m⁵) |
|---|---|---|---|
| AD | 600 | 0.025 | 126914853 |
| BD | 900 | 0.100 | 185910 |
| DC | 150 | 0.150 | 4080.3 |

#### Method
Let $H_D$ be the piezometric head at D. Flows are directed from the higher to the lower head. C (40 m) is the lowest, so DC always carries water to C. B (70 m) is the highest, so B supplies. A (65 m) supplies if $H_D < 65$ m and receives water if $H_D > 65$ m.

Trial with $H_D = 65$ m (no flow in AD): $Q_{BD} = \sqrt{5/185910} = 0.0052$ m³/s in, $Q_{DC} = \sqrt{25/4080.3} = 0.0783$ m³/s out. The outflow is larger than the inflow, so $H_D$ must be lowered below 65 m, and A also supplies D: $Q_{AD} + Q_{BD} = Q_{DC}$.

| $H_D$ (m) | $Q_{AD}$ | $Q_{BD}$ | $Q_{DC}$ | $Q_{AD} + Q_{BD} - Q_{DC}$ |
|---|---|---|---|---|
| 64 | 0.00009 | 0.00568 | 0.07669 | -0.07092 |
| 50 | 0.00034 | 0.01037 | 0.04951 | -0.03879 |
| 45 | 0.00040 | 0.01160 | 0.03501 | -0.02301 |
| 40.69 | 0.00044 | 0.01256 | 0.01300 | -0.00001 |

The balance is at $H_D = 40.69$ m.

#### Discharges
$$
Q_{AD} = \sqrt{\frac{65 - 40.69}{126914853}} = 0.000438\ \text{m}^3/\text{s} = 0.44\ \text{l/s}\quad(\text{A to D})
$$
$$
Q_{BD} = \sqrt{\frac{70 - 40.69}{185910}} = 0.01256\ \text{m}^3/\text{s} = 12.56\ \text{l/s}\quad(\text{B to D})
$$
$$
Q_{DC} = \sqrt{\frac{40.69 - 40}{4080.3}} = 0.01299\ \text{m}^3/\text{s} = 12.99\ \text{l/s}\quad(\text{D to C})
$$
Check: $0.438 + 12.556 = 12.994 \approx 12.99$ l/s.

**Answer:** $Q_{AD} = 0.44$ l/s (A to D), $Q_{BD} = 12.56$ l/s (B to D), $Q_{DC} = 12.99$ l/s (D to C); $H_D = 40.69$ m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does pipe DC always carry water to C?
   A. DC is the largest diameter
   B. C is the lowest reservoir (40 m)
   C. C is the highest reservoir
   D. DC is the longest pipe
   Answer: B. Water flows from higher to lower head, and C is below every other level. (Key point: Which reservoir receives)

2. At H_D = 65 m, Q_BD = 0.0052 and Q_DC = 0.0783. What follows?
   A. Lower H_D, so A also supplies D
   B. Raise H_D, so A receives
   C. H_D = 65 is correct
   D. Close pipe BD
   Answer: A. Outflow is greater than inflow, so the junction head drops below 65 m and A also feeds D: Q_AD + Q_BD = Q_DC. (Key point: Trial at H_D = 65 m)

3. What is the balanced H_D and the flow in DC?
   A. H_D = 65 m, Q_DC = 78 l/s
   B. H_D = 70 m, Q_DC = 13 l/s
   C. H_D = 40 m, Q_DC = 0
   D. H_D = 40.69 m, Q_DC = 12.99 l/s
   Answer: D. Q_DC = sqrt((40.69 - 40)/4080.3) = 0.01299 m^3/s. (Key point: Resulting heads and flows)

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