Syringe pumps such as in Problem 2.4 are limited by the force that the linear motor can apply to the plunger. To guide the design of a new line of pumps, it is desired to predict the forces for syringes of various sizes. Derive a general expression for the force that must be applied to the syringe in Fig. P2.4, assuming that the tubing is horizontal and the plunger itself is frictionless.

Data from Problem 2.4:

Suppose that a laboratory experiment requires that an aqueous solution be delivered to an open container at a constant flow rate of 100 μl/min for 30 min. A syringe pump is available, which has a motor and gear drive that will advance the plunger of any syringe at a set speed. As shown in Fig. P2.4, the syringe diameter is D_s and the pusher speed is U_s. The syringe will be connected to plastic tubing with a length L = 50 cm and a diameter D = 0.86 mm. There may be a height difference between the ends of the tubing. A syringe size must be chosen.

(a) According to the pump manufacturer, U_s can be controlled from 0.08 to 80 mm/min. Three syringe sizes available in the particular lab are 1 ml (D_s = 4.8 mm), 5 ml (D_s = 12.1 mm), and 50 ml (D_s = 26.7 mm). Which would be best?

(b) If the tubing inlet and outlet are at the same height, what will |ΔP| be within the tubing? Will it be affected by the size of the syringe?

(c) If the tubing outlet is raised by 10 cm, what will the new |ΔP| be?

Transcribed Image Text:

Figure P2.4 Syringe pump. D₂ Us