Bernoulli's equation/pressure question

[Senya]

Homework Statement

Water at 20°C flows through a capillary tube with an inside radius of 0.17 mm and a length of 5.9 cm. If the volume flow rate through the capillary is 1.9 cm3/s, what is the pressure difference between the two ends of the capillary? Give your answer in kPa. The viscosity of water at 20°C is 1.0 x 10-3 Pa s.

Homework Equations

P(1) + 1/2pv^2 = P(2) + 1/2pv^2
(p1-p2) = 1/2pv2^2-1/2pv1^2

The Attempt at a Solution

i tried using the second equation for difference in pressure but what i get is zero which is unfortunately wrong. Aside from that, using the bernouli's equation number 1 requires for variables i don't have.

 

[MexChemE]

Hi, Senya, and welcome to PF!

The Bernoulli equation assumes incompressible flow, and, if the inside radius of the capillary tube is constant, the velocities at the start and end points will be the same. Try assuming the capillary tube is vertical and use its length to calculate the change in gravitational potential energy, which will cause a change in pressure.

 

[SteamKing]

Homework Statement

Water at 20°C flows through a capillary tube with an inside radius of 0.17 mm and a length of 5.9 cm. If the volume flow rate through the capillary is 1.9 cm3/s, what is the pressure difference between the two ends of the capillary? Give your answer in kPa. The viscosity of water at 20°C is 1.0 x 10-3 Pa s.

Homework Equations

P(1) + 1/2pv^2 = P(2) + 1/2pv^2
(p1-p2) = 1/2pv2^2-1/2pv1^2

The Attempt at a Solution

i tried using the second equation for difference in pressure but what i get is zero which is unfortunately wrong. Aside from that, using the bernouli's equation number 1 requires for variables i don't have.

Which variables don't you have?

Also, remember that Bernoulli's equation is valid only for incompressible and inviscid flows. The viscosity of water is not zero, so there will be some friction losses as water flows through the capillary tube. You must account for these friction losses by modifying the Bernoulli equation.