SLIP FACTOR AND PRESSURE COEFFICIENT

In the ideal velocity diagrams, we had assumed that v_w2 = u₂. However, in actual operation, this condition is not satisfied in actual practice due to secondary flow effects. Actually, v_w2 < u₂. The difference (u₂ – v_w2) is called the slip. The slip factor is defined as the ratio of actual whirl component to the ideal whirl component and is denoted by ϕ_s.

The total head pressure ratio is given by,

Substituting the value of (T₀₂ – T₀₁) from Eq. (10.5), we have

The actual work done per kg of air is given by:

 

c_p (T_02′ – T₀₁) = u₂v_w2

The actual work done per kg of air by the compressor is always greater than u₂v_w2 due to fluid friction and windage losses. Therefore, the actual work is obtained by multiplying u₂v_w2 by the factor ϕ_w, called the work factor or power input factor.

c_p (T_02′ – T₀₁) = ϕ_wu₂v_w2

Eq. (10.29) becomes

Now, v_ω2 = ϕ_su₂

The pressure coefficient is defined as the ratio of isentropic work to Euler work and is denoted by ϕ_p.

Using Eq. (14.5) and assuming radial vanes of impeller, i.e., v_w2 = u₂, we get

Using Eqs (14.28) and (14.30), we get