Froude Number And Reynolds Number 343l1f

Froude Number Froude number (Fr), in hydrology and fluid mechanics, dimensionless quantity used to indicate the influence of gravity on fluid motion. It is generally expressed as Fr = v/(gd)1/2, in which d is depth of flow, g is the gravitational acceleration (equal to the specific weight of the water divided by its density, in fluid mechanics), v is the celerity of a small surface (or gravity) wave, and Fr is the Froude number. When Fr is less than 1, small surface waves can move upstream; when Fr is greater than 1, they will be carried downstream; and when Fr = 1 (said to be the critical Froude number), the velocity of flow is just equal to the velocity of surface waves. The Froude number enters into formulations of the hydraulic jump (rise in water surface elevation) that occurs under certain conditions, and, together with the Reynolds number, it serves to delineate the boundary between laminar and turbulent flow conditions in open channels. In open channel hydraulics, the Froude number is a very important non-dimensional parameter.The Froude Number is a dimensionless parameter measuring the ratio of the inertia force on a element of fluid - to the weight of the fluid element, the inertial force divided by gravitational force.

The Froude Number can be expressed as

Fr = v / (g hm)1/2

(1)

Where: Fr = Froude number v = velocity (m/s) g = acceleration of gravity (9.81 m/s2) hm = hydraulic mean depth or characteristic length (m)

The Froude Number is relevant in fluid dynamic problems where the weight (gravitational force) of the fluid is an important force. In general this is the situation for free surfaces like cold windows and hot radiators - or flow in open conduits like water channels, sewer pipes . It is used when calculating momentum transfer in general and open channel flow and wave and surface behavior in particular. The Froude Number is important when analyzing flow in spillways, weirs, channel flows, rivers and in ship design.

Hydraulic Mean Depth Hydraulic mean depth can be calculated as

hm = A / T

(2)

Where: hm = hydraulic mean depth (m) T = width of conduit or channel open surface (m) A = cross sectional area of filled flow in conduit or channel (m2) Note that the hydraulic radius (or diameter) commonly used in fluid mechanics relates the flow area to wetted perimeter.

Example - Hydraulic Mean Dept in an Open Rectangular Channel

The width of an open channel is 10 m. The depth of the water in the channel is 2 m. The mean dept can be calculated as hm = ((10 m) * (2 m)) / (10 m) = 2m

Reynolds Number Reynolds number, in fluid mechanics, a criterion of whether fluid (liquid or gas) flow is absolutely steady (streamlined, or laminar) or on the average steady with small unsteady fluctuations (turbulent). Whenever the Reynolds number is less than about 2,000, flow in a pipe is generally laminar, whereas, at values greater than 2,000, flow is usually turbulent. Actually, the transition between laminar and turbulent flow occurs not at a specific value of the Reynolds number but in a range usually beginning between 1,000 to 2,000 and extending upward to between 3,000 and 5,000.

In 1883 Osborne Reynolds, a British engineer and physicist, demonstrated that the transition from laminar to turbulent flow in a pipe depends upon the value of a mathematical quantity equal to the average velocity of flow times the diameter of the tube times the mass density of the fluid divided by its absolute viscosity. This mathematical quantity, a pure number without dimensions, became known as the Reynolds number and was subsequently applied to other types of flow that are completely enclosed or that involve a moving object completely immersed in a fluid.

Reynolds Number

The Reynolds number is an experimental number used in fluid flow to predict the flow velocity at which turbulence will occur. It is described as the ratio of inertial forces to viscous forces. For flow through a tube it is defined by the relationship:

The parameters are viscosity η, density ρ and radius r. The suggested number of 2000 is used for the application to blood flow for the example of the aorta. Another approach is to define a variable Reynolds number in of the maximum velocity for laminar flow in a tube by

and characterize the condition for turbulence as the condition when the Reynolds number reaches a critical value like 2000. For a more general approach to turbulence when objects move through a fluid, the relation takes the following form:

where L is a characteristic length associated with the object.

Turbulence in flow is not something that can be calculated precisely, but the concept of the Reynolds number is a helpful one for general engineering of fluid flow problems. It can have some predictive power when measurements are made for a particular geometry to establish an experimental Reynolds number, and can then be helpful in scaling up the size of that geometry.

NAMEI POLYTECHNIC INSTITUTE

COLLEGE DEPARTMENT 123 A. Mabini St., Mandaluyong City

SHIP’S MOTION IN WAVES NA 12 ASSIGNMENT NO.2

FROUDE NUMBER & REYNOLDS NUMBER

Submitted by:

Josefa Carmelli A. Abejar (BSNAMarE 3-B)

Submitted to:

Engr. Reynaldo D. Lupague (Intructor)