A pressure transducer is connected across an orifice as shown. The pressure at the upstream pressure tap is p₁, and the pressure at the downstream tap is p₂. The pressure at the transducer connected to the upstream tap is p_T,1 and to the downstream pressure tap, p_T,2. Show that the difference in piezometric pressure defined as (p₁ + γz₁) − (p₂ + γz₂) is equal to the pressure difference across the transducer, p_T,1 − p_T,2.

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Pi PT. 1 PT, 2 Vertical P2