Tower Drain

Gravity drain and jet model for the MEAM 3470 water tower, fit to our Activity 3 runs.

Lab 2, Activity 3 · Oct 23, 2026

Tower

Height differential

Bucket bottom to the exit. Chips are the heights we tested; jet distances were measured at 1.63 m.

Starting water depth

Exit

Nozzle

No nozzle15.9 mm Big nozzle4.75 mm Small nozzle4.00 mm Custom6.00 mm

Jet

Nozzle angle

deg

Exit height above floor

Scale by our measured distances (0.37 for the big nozzle, 0.58 for the small one)

Drain it

Side view, drawn to scale

Time0.0s

Water depth14.0cm

Flow rate0.00L/min

Jet distance0.00m

Jet distance over time

Flow rate vs height

Lines model, dots measured

Compare exits

Model

Q = C_d A_e √(2g(H + z))Energy balance from the water surface to the exit. C_d lumps every loss.

t = 2A_b (√(H+z₀) − √H) / (C_d A_e √(2g))Time to drain from depth z₀, from dz/dt = −Q/A_b.

x = (v cos θ / g)(v sin θ + √(v² sin²θ + 2g y₀))Drag free jet range, v = C_d √(2g(H + z)).

C_d = 1 / √(1 + ΣK (A_e/A_t)²)Nozzle prediction: tube losses shrink with tube speed squared.

Bucket diameter0.290 m
Hose inner diameter15.9 mm (5/8 in)
Tube and fitting loss ΣK27.6
C_d, no nozzle (fit, 1.84 and 2.80 m)0.187
C_d, big nozzle (measured)0.998
C_d, small nozzle (measured)0.887

Test data

Measured Oct 2026, bucket depth change over a timed run

The 0.96 m no nozzle run is left out of the fit: it drained slower than the big nozzle at the same height, which a restriction cannot cause, so that run likely had a partly closed valve or trapped air. Starting depth for the nozzle runs was not recorded and is taken as 11.5 cm. Jet distances were measured with the bucket at 64 in (1.63 m); water depth (taken as 7 cm) and launch angle were not recorded.