How come this statement is invalid
Bernoullis principle states that the pressure in a fluid is
directly proportional to its velocity
Bernoulli’s Principle
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The sum of pressure energy, kinetic energy, and potential energy per unit mass is always constant for the streamline flow of a non-viscous and incompressible fluid.
Consider,
A1 − Area of cross-section at B
P1 − Pressure at A1
h1 − Height of B
h2 − Height of D
A2 − Area of cross-section at E
P2− Pressure at A2
v1 − Speed at B
v2 − Speed at D
BC = v1Δt
DE = v2Δt
Δt − Time interval
Work done (BC), W1 = P1A1 (v1Δt) = P1ΔV
Work done (DE), W2 = P2A2 (v2Δt) = P2ΔV
Work done on fluid = W1 − W2
= (P1 − P2) ΔV
Change of gravitational potential energy, ΔU = ρgΔV (h2 − h1)
Change in kinetic energy, 
According to work-energy theorem,
General expression for Bernoulli’s equation,
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Bernoulli’s equation does not hold for non-steady flows.