Pressure Drop Through an Orifice as Measured by a Manometer.

By: Austin Thompson

As part of: BIEN 301

February 13, 2007

Problem:

Water at 20°C flows through the orifice shown in figure P6.154, which is monitored by a mercury manometer. If d = 3cm…

a) What is h when the flow rate is 20 m3/h

b) What is Q in m3/h when h = 58cm

Required:

Find h when Q = 20 m3/h

Find the volumetric flow rate when h is given to be 58 cm.

Assumptions

• Laminar Flow

• Liquid

• Incompressible

• Frictionless pipe

• Thin plate (type) orifice

Sketch

Solution

To solve for h, we must have Cd, d, D, ΔP, ReD, V, β, and Q.

We are given d, and Q, from which we can derive the others as follows:

/86.7

403.

3600120

A

QV .6 2

3

smm

sh

hm

D

d

Part a)

With the Reynolds Number now solved for, we can go to figure 6.41 and find that Cd is about 0.605.

Now for the Reynolds Number:

214,392001.

)05)(.86.7(998Re D

VD

Using these Values, the following equation can be solved. Note that ΔP = (pmercury-pwater)(g)(h).

cmh

hACQ Ptd

5.59 :yieldsh for Solving

6.1

998/)81.9)(99813550(2)03(.

4605.

3600

204

22/1

1

/24

Part b)

Part b asks us to find Q when h is a known value of 58 cm.

Using the same equation from part a…

hmsmQ

ACQ Ptd

/7.19or /0054. :yields Qfor Solving

6.1

998/)58)(.81.9)(99813550(2)03(.

4605.

33

422/1

1

/24

Biomedical Application

This problem shows relationship in pressures across an orifice. Given that this example does have perfectly rounded corners and given dimensions, it could be compared to something in the body. A blood clot could be described as an orifice, only with more complex forms of exemplification. Knowing how to calculate pressure changes in an artery or vein may be vital knowledge in saving someone’s life.