Problem Description

The z force for my model appears unusually large. Why and how is it calculated?

Background

In order to understand why the z force appears unusually large you need to understand how the z force is calculated. The information below is taken from the HAMMER help document titled, "Transient Forces" and explains this information. For the full document you can go to Help > HAMMER Help inside the software and do a search for the article.

The z force is calculated at a node by finding what is called a control volume. The control volume is defined as being centered around a node which can be internal (associated with multiple pipess) or external (at the end of exactly one pipe) (see the illustrations below). Based on this volume the weight of the water is determined using the information below.

Net force on the liquid in CV = rate of increase of momentum within CV + momentum flowrate out of CV boundary surface (CS)

Therefore, after collapsing the CV onto the junction or node:

r g Si A_i (H_i - Z) n _i + R = r Si (- Q_i v _i)

where the subscript i refers to the i^th pipe emanating from the node, r is mass density, g is acceleration due to gravity, H is head, Z is elevation, n is the unit inner normal to the CS, A is cross-sectional area, R is the resultant force exerted by the pipe on the liquid, t is time, v is the fluid velocity, and Q is the flowrate towards the node. Note that any boldfaced underlined quantity is a vector.

By rearranging (), it follows that the reaction force on the pipe, applied by the liquid, is given by the vector formula:

P = -R = r Si A_i [ v_i² + g (H _i - Z) ] n_i

where s_i = +1, if the flow in the branch is directed towards the node, and -1 otherwise. On account of the discretization involved, this force is apportioned equally to each of the end points situated at the node.

The first term on the right-hand side of (), which involves v, is associated with momentum flowing across the boundary CS. All terms are functions of time, except for the transverse component of weight which acts in the downward direction -k, where k is a unit vertical upward vector. The longitudinal (or axial) component of weight (if any), a body force on the CV, is already accounted for in the hydraulic transient equations used by Bentley HAMMER V8i to solve for flow/velocity and head/pressure at each instant.

In terms of the Cartesian coordinates, with z being measured vertically upward, the magnitude of the resultant force P = (P_x, P_y, P_z) = -R = (-R_x, -R_y, -R_z) on the pipe is given by:

P = R = |-R| = [R_x² + R_y² + R_z²] ^0.5

For instance, in the case of an internal node as in Figure C-1 with N = 2, vertical pipes meeting at an angle of 180 degrees, and steady flow, then the magnitude of the resultant is given by the relation rg | H₂ A₂ - H₁ A₁|. For steady flow in a vertical pipe discharging to atmosphere through an orifice at its top end as in Figure C-2, the resultant downward force on the pipe is rQ|V - v|, with Q, V, and v being the flow and velocity at the vena contracta and in the pipe, respectively.

The result of the force computations may be restricted to periodic times, as indicated in Transient Solver Calculation Options > Report Times. If the forces are enabled in the Run Dialog, a table of maximum forces - over all time steps regardless of report period - is constructed in the output log with columns: Node, Time, Magnitude, F_x, F_y, and F_z. In the report database, two tables, Force_History and Force_Maxima, are created.

Solution

The z force for your model can appear unusually large if you have long pipes that are larger in size because these types of pipes will make the control volume larger, which would make the weight of the water larger. This would cause the large downward force due the pull of gravity on that volume of water.

See Also

Transient Force Calculations in HAMMER