VM124

VM124
Discharge of Water from a Reservoir

Overview

Reference: K. Brenkert, Jr., Elementary Theoretical Fluid Mechanics, John Wiley and Sons, Inc., New York, NY, 1960, pg. 224, ex. 4.
Analysis Type(s): Thermal (pressure) Analysis (ANTYPE = 0)
Element Type(s): Coupled Thermal-Fluid Pipe Elements (FLUID116)
Input Listing: vm124.dat

Test Case

Water (density ρ, viscosity μ) flows from a large reservoir into a long piping system. Determine the Reynold's number Re and the flow rate w for pipes of friction factor f and diameter d. The loss coefficients for the sharp-edged entrance and 90° elbow are K1 and K2, respectively.

Material PropertiesGeometric PropertiesLoading
ρ = 1.94 lb-sec2/ft4
μ = 2.36 x 10-5 lb-sec/ft2
H = 20 ft
1 = 20 ft
2 = 70 ft
3 = 10 ft
d = 0.25 ft
K1 = 0.5
K3 = 0.9
f = 0.028 for 105 < Re < 106
g = 32.2 ft/sec2

Analysis Assumptions and Modeling Notes

The reservoir head is given by (H -  3) = 10 ft. This is applied as a pump head within a short (0.01 ft, to minimize friction) horizontal element. The acceleration input accounts for the vertical flow. The exit pressure and the water surface pressure is defined to be zero. An iterative solution is required. A friction factor of 0.025 (input for MU) is assumed for a starting value.

Results Comparison

TargetMechanical APDLRatio
w, lbfsec/ft0.8980.930[1]1.036
Re1.94 x 105 2.01 x 105 1.035

  1. w is given by nodal flow at node 1.