4.3 A simple flow in a straight conduit

= 0.4

Figure: General simple conduit description

A simple and most common component is a straight conduit as shown in Figure . The simplest conduit is a circular pipe which would be studied here first. The entrance problem and the unsteady aspects will be discussed later. The parameters that the die casting engineers interested are the liquid metal velocity, the power to drive this velocity, and the pressure difference occur for the required/desired velocity. What determine these parameters? The velocity is determined by the pressure difference applied on the pipe and the resistance to the flow. The relationship between the pressure difference, the flow rate and the resistance to the flow is given by the experimental equation (). This equation is used because it works². The pressure difference determined by the geometrical parameters and the experimental data which expressed by ³ which can be obtained from Moody's diagram. = 0.5

Figure: Moody's diagram

(4.1)

Note, head is energy per unit weight of fluid (i.e. Force x Length/Weight = Length) and it has units of length. Thus, the relationship between the Head (loss) and the pressure (loss) is

(4.2)

The resistance coefficient for circular conduit can be defined as

(4.3)

This equation is written for a constant density flow and a constant cross section. The flow rate is expressed as

(4.4)

The cross sectional area of circular is , using equation () and substituting it into equation () yields

(4.5)

The equation () shows that the required pressure difference, , is a function of which demonstrates the tremendous effect the diameter has on the flow rate. The length, on the other hand, has mush less significant effect on the flow rate.

The power which requires to drive this flow is give by

(4.6)

These equations are very important in the understanding the economy of runner design, and will be studied in Chapter in more details.

The power in terms of the geometrical parameters and the flow rate is given

(4.7)