What condition gives complete removal of a particle in an ideal horizontal-flow tank?

Settling time H/vs equals flow-through time L/vh

Settling velocity equals horizontal velocity

Detention time is exactly 1 hour

Why is Stokes' law acceptable for the 0.02 mm particle?

Re = 0.007, which is less than 1

The particle is heavier than water

How is the recommended flow velocity obtained from vs?

vh = vs × L/H = 0.03597 × 20/2.5 = 0.288 cm/s

Why is 0.173 m/min checked against 0.3 m/min?

To make sure the flow does not scour settled sludge

To make sure water does not freeze

Asked 2/30
2066 Bhadra (old course)

Settling tank 20 m x 2.5 m; velocity for 0.02 mm

Short answer

For complete removal, horizontal velocity v_h = v_s × L/H. Stokes' settling velocity is 0.036 cm/s (Re<1). With L=20 m, H=2.5 m, v_h = 0.288 cm/s (17.3 cm/min).

In a continuous flow settling tank 20 m long and 2.5 m deep, what velocity of water would you recommend for effective removal of 0.02 mm particles at 25°C? Assume specific gravity of particles = 2.65 and kinematic viscosity of water = 0.01 cm $^2$ /sec.

For complete removal in an ideal horizontal-flow tank, the particle must settle the depth $H$ in the time the water takes to flow the length $L$ :

\frac{H}{v_s}=\frac{L}{v_h}\ \Rightarrow\ v_h=v_s\,\frac{L}{H}

Step 1: Settling velocity of the 0.02 mm particle

$d=0.002$ cm, $S_s=2.65$ , $\nu=0.01$ cm²/s (given):

v_s=\frac{981\times1.65\times0.002^2}{18\times0.01}=0.03597\ \text{cm/s}\quad(Re=0.007<1)

Step 2: Horizontal velocity

$L=20$ m, $H=2.5$ m:

v_h=0.03597\times\frac{20}{2.5}=0.2878\ \text{cm/s}=17.27\ \text{cm/min}=0.173\ \text{m/min}

This is below the 0.3 m/min limit for scour, so it is acceptable.

Answer: the velocity of flow should not exceed 0.288 cm/s (17.3 cm/min).

✓ Answer checked by Claude Opus 5.5 (high effort)

Settling tank 30 m x 3 m; velocity for 0.02 mm · Water Supply Engineering, chapter 6 · asked 2×
Settling tank 20 m long, 3.5 m deep; 0.02 and 0.01 mm · Water Supply Engineering, chapter 6 · asked 3×
Settling tank 30 m x 3 m, 0.02 mm at 25°C; 0.01 mm at 10°C · Water Supply Engineering, chapter 6 · asked 3×
Settling tank 30 m x 3 m, 0.03 mm at 25°C; 0.025 mm at 20°C · Water Supply Engineering, chapter 6 · asked 3×
Settling tank 30 m x 3 m, 0.02 mm, SG 2.50 · Water Supply Engineering, chapter 6
Settling velocity of silica particle 0.02 cm at 20°C · Water Supply Engineering, chapter 6
Settling tank 15 x 4 x 2.5 m, 96% of 0.015 mm · Water Supply Engineering, chapter 6
Continuous flow sedimentation tank particle size · Sanitary Engineering, chapter 7

All Water Supply Engineering chapter 6 questions →

Settling tank 20 m x 2.5 m; velocity for 0.02 mm

Step 1: Settling velocity of the 0.02 mm particle

Step 2: Horizontal velocity

Related questions