A simple flow system to be used for steady-flow tests consists of a constant head tank connected to a length of 4-mm-diameter tubing as shown in Fig. P6.89. The liquid has a viscosity of \(0.015 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\), a density of \(1200 \mathrm{~kg} / \mathrm{m}^{3}\), and discharges into the atmosphere with a mean velocity of \(2 \mathrm{~m} / \mathrm{s}\).

(a) Verify that the flow will be laminar.

(b) The flow is fully developed in the last \(3 \mathrm{~m}\) of the tube. What is the pressure at the pressure gage?

(c) What is the magnitude of the wall shearing stress, \(\tau_{r}\), in the fully developed region?

Figure P6.89

Pressure gage 3 m Diameter 4 mm