Amplitude of water pouring sound

We experimentally investigate the amplitude of the common sound heard when we pour water, tea, or coffee on a filled receptacle. Using water jets from circular nozzles, we find that pouring is audible when the nozzle distance from the free surface is above one-third of the jet breakup length. The sound amplitude increases with the steepness of the jet corrugation, informing that thin jets are louder than thick ones for a given pouring height. Since the jet corrugation is related to the air entrainment rate, the sound of pouring can serve as a practical noninvasive probe in aeration processes. After the jet breaks up into drops impacting on the free surface, the pouring sound amplitude increases with the nozzle diameter, unlike before breakup.

Figure 1

Water pouring on a filled cylindrical cup from (a) a commercial plastic bottle and (b) a teapot. (c) Model water pouring from a smooth brass tube. Scale bar: 2 cm.

Figure 2

(a) Experimental setup. The nozzle diameter is much smaller than the cup and tank diameters, $d\ll D_c<D_t$. (b) Pressure RMS $\overline{p}$ versus the nozzle distance $l$. Jet breakup occurs at the points indicated by arrows of corresponding color. (c)–(e) Images of plunging jet and bubble plume for $d=3$ mm at $l=3$, 10, and 25 cm, respectively. The breakup length is $l_{\mathrm{B}}=13.3$ cm. Scale bar: 2 cm. Note that the penetration depth of the bubbles decreases with the jet length and reaches a plateau.

Figure 3

(a) Schematics of an unstable jet, depicting the breakup length $l_{\mathrm{B}}$, the wavelength $\lambda$, and the corrugation $\epsilon$. (b) Corrugation versus nozzle distance. (c) Corrugation steepness $\epsilon /\lambda$ versus $l/l_{\mathrm{B}}$. Inset: Breakup length ($•$, left $y$ axis) and characteristic wavelength ($•$, right $y$ axis) versus the jet diameter $d$. The red line is $l_{\mathrm{B}}\propto 2.59d^{3/2}$, and the green line is $\lambda \sim 4.27d$, the latter prefactor being close to the theoretical value 4.51 [23].

Figure 4

Normalized pressure $(\overline{p}-{\overline{p}}_{\mathrm{noise}})/\rho c{u}_0$ versus ${(d/R_{\mathrm{h}})}^2(\epsilon /\lambda -\alpha )$ before jet breakup ($l<l_{\mathrm{B}}$). The dashed line is Eq. (2), and has a slope of $k=1.35\times {10}^{-2}$ ($r^2=0.97$) for a detection threshold of $\alpha =0.02$. Inset: Pressure RMS versus air entrainment rate $Q_{\mathrm{air}}=\pi u_{0}d\epsilon$.

Figure 5

Normalized pressure $\overline{p}/\rho c{u}_0$ versus the product ${(d/R_{\mathrm{h}})}^2{(l/l_{\mathrm{B}})}^{1/2}$. The dashed line is Eq. (4), which fits the data beyond break-up $l>l_{\mathrm{B}}$ ($r^2=0.99$). Inset: $\overline{p}$ versus $l/l_{\mathrm{B}}$ in logarithmic scale.