What is the Gauge Pressure Just Downstream of a Fan in a Duct System?

[kieranl]

Homework Statement

A duct system that exhausts air of density 1.2kg/m3 from a building out into the atmosphere is shown in fig. A2 (attachment). The air flow is driven by a fan across which is a monometer that reads 2 cm of water. The cross sectional areas of the upstream and downstream ducts are 0.1m2 and 0.2m2 respectively and the flow speed in the upstream duct is 10ms^-1. Assume that air is incompressible and inviscid and that temperature changes in the air are negligible. Take acceleration due to gravity to be 10m/s2

Homework Equations

bernouli equation P + 0.5pV^2 + pgz = constant

The Attempt at a Solution

Im just confused with the third part of the question

c) Determine the gauge pressure just downstream of the fan

I would of thought that the pressure just downstream of the fan would be at atmospheric because the velocity is the same as when it exits the duct? so that would mean gauge pressure = 0Pa... but the answer is -15Pa

Im stuck?

 

[tiny-tim]

Hi kieranl!

(have a rho: ρ and try using the X² tag just above the Reply box )

I would of thought that the pressure just downstream of the fan would be at atmospheric because the velocity is the same as when it exits the duct? so that would mean gauge pressure = 0Pa... but the answer is -15Pa

Bernoulli's equation works along a streamline …

so follow a streamline from the fan to the outside air … far enough away, the speed will be zero, so the pressure must be higher.