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Bernoulli's Equation Pressure at Blockage

Problem Statement
Bernoulli's equation tells us that a portion of a stream that is slower-moving has a higher pressure than a portion of the same stream that is faster-moving. What would happen if I blocked the flow of two different streams, a faster-moving stream and a slower-moving stream? Why would I experience a higher pressure when blocking the faster-moving stream?
Relevant Equations
$$\frac{p}{\rho} + \frac{v^2}{2} = \text{cst}$$
Would it be because I'm comparing two different streams as opposed to two portions of the same stream?
 
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Can you please describe this system in more detail, with a diagram.
 

haruspex

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if I blocked the flow of two different streams, a faster-moving stream and a slower-moving stream?
If there are two different streams there is no relationship between their pressures. You could add a constant pressure throughout one of the streams and nothing would change in the flow.
 

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