Page 78 - Mechanical Engineers' Handbook (Volume 4)

9 Viscous Flow and Incompressible Boundary Layers 67

The specific speed of pumps and turbines results from combining groups in a dimen-
sional analysis of rotary systems. That for pumps is N s (pump) N Q /e 3/4 and for turbines
1/2 5/4
it is N s (turbines) N power / e , where N is the rotational speed in rad/sec, Q is the
3
volumetric flow rate in m /sec, and e is the energy in J/kg. North American practice uses
N in rpm, Q in gal/min, e as energy per unit weight (head in ft), power as brake horsepower
rather than watts, and omits the density term in the specific speed for turbines. The numerical
value of specific speed indicates the type of pump or turbine for a given installation. These
are shown for pumps in North America in Fig. 20. Typical values for North American
turbines are about 5 for impulse turbines, about 20–100 for Francis turbines, and 100–200
for propeller turbines. Slight corrections in performance for higher efficiency of large pumps
and turbines are made when testing small laboratory units.

9 VISCOUS FLOW AND INCOMPRESSIBLE BOUNDARY LAYERS

In viscous flows, adjacent layers of fluid transmit both normal forces and tangential shear
forces, as a result of relative motion between the layers. There is no relative motion, however,
between the fluid and a solid boundary along which it flows. The fluid velocity varies from
zero at the boundary to a maximum or free stream value some distance away from it. This
region of retarded flow is called the boundary layer.

9.1 Laminar and Turbulent Flow
Viscous fluids flow in a laminar or in a turbulent state. There are, however, transition regimes
between them where the flow is intermittently laminar and turbulent. Laminar flow is smooth,
quiet flow without lateral motions. Turbulent flow has lateral motions as a result of eddies
superimposed on the main flow, which results in random or irregular fluctuations of velocity,
pressure, and, possibly, temperature. Smoke rising from a cigarette held at rest in still air
has a straight threadlike appearance for a few centimeters; this indicates a laminar flow.
Above that the smoke is wavy and finally irregular lateral motions indicate a turbulent flow.
Low velocities and high viscous forces are associated with laminar flow and low Reynolds

Figure 20 Pump characteristics and specific speed for pump impellers. (Courtesy Worthington Cor-
poration)