Loading a barge

Homework Help
1

A rectangular barge 20ft wide by 50ft long by 8ft deep floats empty with a draft of 3ft in a canal lock 30ft wide by 60ft long and water depth 6 ft. if 200000lb of steel is loaded onto the barge what is the new draft? what is the new water depth in the lock?

3

PK Bot’s answer:

  1. ENGINEERING CONTEXT:
    A rectangular barge in a lock is loaded with steel, and by applying buoyancy and volume conservation we identify how the increased weight raises the barge’s draft and causes the lock water level to rise—a design technique important for safely planning vessel loading in constrained waterways.

  2. PHYSICS:
    The dominant effects are that the buoyant force (determined by the hydrostatic pressure distribution) must increase to balance the extra load, and the displaced water causes a rise in the lock’s water level via volume conservation.

  3. ASSUMPTIONS:
    We assume that water is incompressible and of uniform weight density (62.4\ lb/ft^3) and that the barge’s waterplane area remains constant with loading; these simplify the use of Archimedes’ principle and allow an accurate estimate for small changes relative to the lock dimensions.

  4. SOLUTION TECHNIQUE:

  • The barge’s waterplane area is
A=20\ ft\times50\ ft=1000\ ft^2.
  • With an initial draft of 3\ ft, the barge initially displaces
V_i=1000\ ft^2\times3\ ft=3000\ ft^3.
  • Adding 200000\ lb of steel requires an extra displaced water volume of
\Delta V=\frac{200000\ lb}{62.4\ lb/ft^3}\approx3205\ ft^3.
  • The incremental draft is then
\Delta T=\frac{\Delta V}{A}\approx\frac{3205\ ft^3}{1000\ ft^2}\approx3.205\ ft,

making the new draft

T_{new}=3\ ft+3.205\ ft\approx6.205\ ft.
  • The lock floor area is
A_{lock}=30\ ft\times60\ ft=1800\ ft^2.
  • The additional displaced volume from the barge increases the water level in the lock by
\Delta H=\frac{\Delta V}{A_{lock}}\approx\frac{3205\ ft^3}{1800\ ft^2}\approx1.78\ ft,

so the new water depth in the lock becomes

H_{new}=6\ ft+1.78\ ft\approx7.78\ ft.
  1. REFLECTION:
    The analysis, based on Archimedes’ principle and volume conservation, shows that the steel load increases the barge’s draft from 3\ ft to about 6.21\ ft and raises the lock water level from 6\ ft to about 7.78\ ft, a result useful for assessing safe loading and water level impacts in lock design.

To formulate this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2). Below, I have organized the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:

Textbook sections:

  1. Chapter 4.1: Watercraft (HIGHLY RELEVANT)
  2. Chapter 4.3: Archimedes’ Law (HIGHLY RELEVANT)
  3. Chapter 4 Engineering Models: Hydrostatic Equation (RELEVANT)
  4. Chapter 3 Engineering Models: Hydrostatic Equation (RELEVANT)
  5. Chapter 4 Fundamentals: The Wreck of the HMS Herald of Free Enterprise (RELEVANT)

Disclaimer:

See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.