Physics Help

posted by Mathslover Please help

Consider a glass with full of water of mass density ρ=1,000 kg/m3 and height h=20 cm. There's a circular hole in the bottom of the glass of radius r. The maximum pressure that pushes the water back into the hole is roughly (on the order of) p=σ/r, where σ=0.072 N/m is the water's surface tension. This extra pressure comes from the curvature of the water surface, and it tends to flatten out the surface.

Estimate the largest possible radius of the hole in μm such that water doesn't drip out of the glass.

Details and assumptions
The gravitational acceleration is g=−9.8 m/s2 and the glass is placed vertically.
Neglect any other effects that can influence the pressure from other external sources.

  1. bobpursley

    net pressure on hole=weight-pushback
    = densitywater*g*height-.072/radius

    when net pressure=zero, then

    radius=.072/(g*.2*densitywater) meters

    = .46/9.6 millimeters=46.9 micrometers.

    check that

  2. Mathslover Please help

    Sir but 46/9.6 is 4.79 tell the right answer

  3. levina

    1000*9.8*0.2 = 0.072/r
    1960*r = 0.072
    r = 3,673 x 10^(-5) m
    so r = 36,73 μm

  4. levina

    sorry i mean
    r = 3.673 x 10^(-5) m
    so r = 36.73 μm

    haha still confused with . and , :)

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