**
***A barometer, that is, a device that measures pressure, can be constructed from a tube which is open at both ends and shaped like a U. A fluid, like mercury, is placed inside, filling the bottom portion of the U. If the height of the mercury column at one end is greater than at the other end, then the pressure above the liquid on that end is less.*

*A modification of a barometer can be used to measure flow speed. Consider a pipe which carries an inviscid, incompressible fluid moving a speed v and pressure P _{1} far upstream. Barometer 1 does not interrupt the flow, so it measures P_{1}. If Barometer 2 is placed in the flow as shown in the figure below, then the tip of the barometer forms an obstruction in the flow.*

*The flow just in front of the tip comes to stop at what is called a stagnation point. Nevertheless, we can consider the line shown in the figure, which comes to an end at the stagnation point, to be a streamline.*

*The figure below shows a flow with a constriction. The flow far upstream has a speed v _{3}, pressure P_{3}, and a cross-sectional area A_{3}. In the constriction the flow has a velocity v_{4}, pressure P_{4}, and a cross-sectional area A_{4}.*

*For the following problems, letρbe the density of mercury.*

Again, suppose the fluid were replaced with a fluid that had viscosity, but *v _{3}*,

*P*

_{3},

*A*

_{3}, and

*A*

_{4}remained the same. How would the new pressure in the constriction be changed from

*P*

_{4}?