Partially Closed Valve

Figure: A shock as a result of a sudden and partially a valve closing or a narrowing the passage to the flow

The totally closed valve is a special case of a partially closed valve in which there is a sudden change and the resistance increases in the pipe. The information propagates upstream in the same way as before. Similar equations can be written:

$$U_x = U_s + {U_x}^{'}$$ (5.78)

$$U_y = U_s + {U_y}^{'}$$ (5.79)

$$M_x = M_s + {M_x}^{'}$$ (5.80)

$$M_y = M_s + {M_y}^{'}$$ (5.81)

For given static Mach numbers the procedure for the calculation is as follows:

(a)

Assume that ${M_x} = {M_x}^{'} + 1.$

(b)

. Calculate the Mach number $M_y$ by utilizing the tables or Potto-GDC

(c)

Calculate the ``downstream'' shock Mach number $M_{sy} = M_y - {M_y}^{'}$

(d)

Utilizing

$$M_x = \sqrt{T_y \over T_x} \left( M_{sy} \right) + {M_x}^{'}$$

calculate the new ``improved'' M_x

(e)

Check the new and improved M_x against the old one. If it is satisfactory, stop or return to stage (b).