---
title: "Venturimeter as suction device, minimum discharge"
subject: "Fluid Mechanics"
chapter: 6
key: "semester_3/fluid_mechanics:venturi-suction-minimum-discharge"
source: https://www.bctengineer.com/q/semester_3/fluid_mechanics/venturi-suction-minimum-discharge
site: BCT Engineering
---

# Venturimeter as suction device, minimum discharge

Fluid Mechanics · Chapter 6: Flow measurement

- Asked in: 2072 Chaitra, 7 marks
- Video: [venturimeter & derive equation of discharge](https://www.youtube.com/watch?v=oINBqDpvSIc) — GTU MIMP
- Page: https://www.bctengineer.com/q/semester_3/fluid_mechanics/venturi-suction-minimum-discharge
- Whole chapter: https://www.bctengineer.com/md/semester_3/fluid_mechanics/chapter-6

## Question

Figure below shows a venturimeter with its axis vertical and arranged as a suction device. The throat area and the outlet area of the venturi are 0.00025 m² and 0.001 m² respectively. If the venturi discharges into the atmosphere, determine the minimum discharge in the venturi at which flow will occur up the suction pipe. [Figure: vertical venturimeter with a suction pipe from the throat to a water tank below; marked heights 2.0 m, 1.9 m and 1.0 m]

## Short answer

Suction lift assumed 1.9 m; throat pressure must be -1.9 m gauge. Bernoulli from throat to outlet gives Vt^2/(2g)=0.96 m, Vt=4.34 m/s, Qmin=0.00025×4.34≈1.085e-3 m^3/s (1.09 L/s).

## Answer

**Given:** throat area $a_t = 0.00025$ m², outlet area $a_e = 0.001$ m², venturi vertical, discharging to atmosphere.

The figure values (2.0 m, 1.9 m, 1.0 m) are not fully readable, so assume: the throat is $z_t = 1.0$ m above the outlet plane, and the water surface in the suction tank is $H_s = 1.9$ m below the throat.

```text
        inlet
        ||
        ||        <- 
      throat ---- suction pipe (to tank)
        /\          1.9 m lift
       /  \
      outlet (atmosphere) ... 1.0 m below throat
```

**Condition for flow up the suction pipe:** the throat pressure must fall at least to $p_t = -\gamma H_s$ (gauge). The minimum discharge is when $p_t/\gamma = -1.9$ m.

**Continuity:** $V_t = Q/a_t$, $V_e = Q/a_e = V_t/4$.

**Bernoulli, throat to outlet (exit pressure atmospheric):**

$$
\frac{p_t}{\gamma} + \frac{V_t^2}{2g} + z_t = 0 + \frac{V_e^2}{2g} + 0
$$

$$
\begin{aligned}
-1.9 + \frac{V_t^2}{2g} + 1.0 &= \frac{V_t^2}{16\times 2g}\\
\frac{V_t^2}{2g}\left(1 - \frac{1}{16}\right) &= 0.9\\
\frac{V_t^2}{2g} &= 0.96\ \text{m}\\
V_t &= \sqrt{2\times 9.81\times 0.96} = 4.340\ \text{m/s}
\end{aligned}
$$

$$
Q_{min} = a_tV_t = 0.00025\times 4.340 = 1.085\times 10^{-3}\ \text{m}^3/\text{s}
$$

**Answer: minimum discharge $\approx 1.085\times 10^{-3}$ m³/s (about 1.09 L/s)** for the assumed dimensions. General result: $Q_{min} = a_t\sqrt{2g\,(H_s - z_t)\big/\left(1 - (a_t/a_e)^2\right)}$.

## Check yourself

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

1. What throat pressure is needed for water to rise up the suction pipe?
   A. Zero gauge
   B. Equal to the outlet pressure
   C. At least as low as -gamma*Hs (gauge)
   D. Above atmospheric
   Answer: C. The throat pressure must fall to the level that lifts water through the suction height Hs; the minimum discharge corresponds to equality. (Key point: Condition for suction flow)

2. How are throat and exit velocities related?
   A. Ve = Vt/4
   B. Ve = Vt
   C. Ve = Vt/16
   D. Ve = 4Vt
   Answer: A. Ve = Q/ae and Vt = Q/at with ae = 4at, so Ve = Vt/4. (Key point: Continuity)

3. With exit at atmosphere, what does Bernoulli give?
   A. -1.9 + Vt^2/2g = Ve^2/2g + 1.0
   B. 1.9 + Vt^2/2g = Ve^2/2g
   C. -1.9 + Vt^2/2g + 1.0 = Ve^2/2g
   D. Vt^2/2g = Ve^2/2g
   Answer: C. The throat is 1.0 m above the outlet, so the elevation term appears on the throat side. (Key point: Bernoulli throat to outlet)

## Related in Fluid Mechanics

- [Minimum throat diameter of venturimeter](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aventurimeter-minimum-throat-diameter) — Fluid Mechanics, chapter 6
- [Venturimeter with reservoir suction tube](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Aventurimeter-reservoir-lift-height) — Fluid Mechanics, chapter 6
- [Time to discharge pressurised tank](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Apressurised-tank-emptying-orifice) — Fluid Mechanics, chapter 6

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