A siphon may be used to draw a liquid above its level in an open tank or channel and discharge it below that level. Once initiated, the flow is sustained by the height difference. The simplest configuration is an inverted U-tube, as in Fig. P11.13. Assume here that viscous losses are negligible, although that is not always true in real siphons.

(a) After an empty tube has been inserted into the tank, how much suction must be applied at position C to start the flow?

(b) If the flow, once started, is turbulent, what will the mean velocity U in the tube be?

(c) Show that during operation the pressure P_B at position B is subatmospheric.

(d) Lowering the outlet will increase the flow rate. However, cavitation might eventually make the siphon unreliable. That can be avoided if the pressure everywhere exceeds P_V, the vapor pressure of the liquid. What limits would that place on H_C and U?

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Air Po Liquid Hв HA Figure P11.13 Open tank with siphon. A B Hc