The “spherical” Pitot probe shown is used to measure the flow velocity in hot water (ρ = 965 kg/m³). Pressure taps are located at the forward stagnation point and at 90° from the forward stagnation point. The speed of fluid next to the surface of the sphere varies as 1.5 V₀ sin θ, where V₀ is the free-stream velocity and θ is measured from the forward stagnation point. The pressure taps are at the same level; that is, they are in the same horizontal plane. The piezometric pressure difference between the two taps is 3 kPa. What is the free-stream velocity V₀?

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V = 1.5 V, Ap = 3 kPa