# The coefficient of entry (CE)

For normal entry-pieces not all the static suction is used to accelerate the air to the velocity prevailing in the downstream duct. Some of the potential energy of the suction set up is wasted in offsetting losses due to turbulence and friction. It is customary to express these losses in terms of the steady velocity pressure in the downstream duct, after any vena — contracta. Thus, the loss due to eddies formed at the vena-contracta can be written as Ј multiplied by this velocity pressure, where C, is obviously less than unity.

The fact that there is a reduced area. A’, available for airflow at the vena-contracta gives rise to the concept of a coefficient of area, defined by

CA = A’I A 3 CO CO 0

 (3)  VP(= SP)

 3 CO CO CP

 Distance along the duct SP (= VP)

(b)

Fig. 15.5 Airflow into a suction opening, with and without loss.

Where A is the cross sectional area of the duct.

There is also the concept of a coefficient of velocity. This arises from the fact that the velocity at the vena-contracta is less than that which would be attained if all the static pressure were to be converted into velocity. There is some friction between the air flowing

Through the vena-contracta and the annular pocket of turbulence which surrounds it. This is consequent on the energy transfer needed to maintain the eddies and whorls within the pocket. The coefficient of velocity is defined by

Actual velocity at the vena-contracta velocity which would be attained at the same section in the absence of losses

Since the quantity flowing is the product of velocity and area it can be seen that a flow or entry coefficient CE, may be inferred as the product of the coefficients of velocity and area

C%= Cy x Ca

Thus, Q, the actual rate of flow of air entering the system, may be expressed by Q = CexQ’

Where Q’ is the theoretical rate which would flow if no loss occurred. It may also be written as

Q = Ce(A x V)

But V = 1.291 V/?v, the theoretical maximum possible velocity, where pv is equivalent to the static suction set up in the plane of the vena-contracta. Thus,

Q = Ce(A x 1.291 Vpv)

Posted in Engineering Fifth Edition