Low Speed Application

In Low Speed application, especially in civil engineering, it is usual to express energy as a Head, with each of the terms in Eqn. 3.66 having the units of a Length, m. This is done by dividing the equation throughout by g. Thus,

$$\left({u \over g}~+~{p \over {\rho~g}}+~z~+~{V^2 \over {2g}} \right)_1~ =~\left({u \over g}~+~{p \over {\rho g}}~+z~+~{V^2 \over {2g}} \right)_2~-{q \over g}~+{w_s \over g}$$ or

$$\left({u \over g}~+~{p \over \gamma}+~z~+~{V^2 \over {2g}} \right)_1~ =~\left({u \over g}~+~{p \over \gamma}~+z~+~{V^2 \over {2g}} \right)_2~-{h_q}~+{h_s}$$ (3.68)

The term $p \over \gamma$ is called the Pressure Head and $V^2 \over {2g}$ the velocity Head. Terms h_q and h_s represent the heat added and shaft work converted to "head" units.

If we consider a simple pipe flow without the shaft work then the equation becomes

$$\left(~{p \over \gamma}+~z~+~{V^2 \over {2g}} \right)_1~=~\left(~{p \over \gamma}+~z~+~{V^2 \over {2g}} \right)_2~+~{{u_2~-~u_2~-q} \over g}$$ (3.69)

The terms within the parenthesis is what is called the Total Head or Available Head. Clearly with the flow some available head is lost because of friction and heat transfer. It is a common practice to use the above equation in the following form-

$$\left(~{p \over \gamma}+~z~+~{V^2 \over {2g}} \right)_1~=~\left(... ...gamma}+~z~+~{V^2 \over {2g}} \right)_2~+~h_{friction}~-~h_{pump}~+~h_{turbine}$$ (3.70)

The losses that take place between "inlet" i.e.,1 and "outlet" i.e., 2 are obtained through measurements and correlations.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney