Radial Inflow Velocity to a Tank Drain: 04-BS-7, December 2014, Q4

Question 4 — Radial Inflow Velocity to a Tank Drain (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Flow rate, Q	0.300 L/s
Radius of interest, r	100 mm

Find. The velocity V in the tank at r = 100 mm from the hole.

Fig. Q4 — water approaches the drain hole radially; the imaginary hemispherical control surface of radius r = 100 mm (dashed) is the surface through which all of Q must pass.

Approach. By continuity, the same flow rate Q passes through every concentric hemispherical control surface surrounding the hole; that surface's area at radius r is 2πr² (a hemisphere, since the tank floor bounds the flow to the upper half-space only).

Hemispherical surface area at r = 100 mm. $$A = 2\pi r^2 = 2\pi(0.100)^2 = \boxed{0.06283\text{ m}^2}$$
Velocity from continuity. $$V = \frac{Q}{A} = \frac{3.00\times10^{-4}}{0.06283} = \boxed{4.775\times10^{-3}\text{ m/s} = 4.78\text{ mm/s}}$$

Quantity	Result
Control-surface area at r = 100 mm	0.0628 m²
Velocity, V	4.78 mm/s

Question 4 of 13: Radial Inflow Velocity to a Tank Drain

Question 4 — Radial Inflow Velocity to a Tank Drain (5 marks)