Flow either side of a t-piece is shown in Figure 1. All flows are in the horizontal plane. Pitot tube flow meters with pressure measurements are fitted to two of the branches (top and RHS) while the other branch (LHS) has a sudden flow contraction. Pressures are measured at 4 points (labelled 1-4). The loss coefficient of the contraction connector K_L,cc is known but the loss coefficient of the T-piece K_L,TP is not. The known values are given in Table 2. In your calculations use 1000 kg/m³ as the density of water.

 

P1	9180 Pa		D1, D3, DTP	16 mm
P2	10820 Pa		KL,CC  *	0.4
P3	7840 Pa		DA	11 mm
P4	8470 Pa		r (water)	1000 kg/m3
g	9.81 m/s2		m (water)	1.2 x 10-3 Nsm-2

* Loss coefficient in contraction is based on the higher velocity

Table 2 Data for question 1

Calculate the following (you may assume major losses are negligible):

a) The velocities in the flow meters V₁ and V₃

b) The velocity after the contraction V_A

c) The loss coefficient of the T-piece K_L,TP (hint consider the flow between p₁ and p₃) where K_L,TP is based on the outlet velocity

d) The pressure after the contraction p_A

 

Flow meter 1 2 Point A D3 DTP. DA contraction T-piece connector Flow meter 2 conector