Housewives face a typical problem when cleaning the house. Sometimes when they are wiping the floorwith water, the water from the bucket spills over. This water can form a puddle on the ground and can

Question

Housewives face a typical problem when cleaning the house. Sometimes when they are wiping the floorwith water, the water from the bucket spills over. This water can form a puddle on the ground and canbe quite a menace to clean. It can be assumed that the water has spread out on the ground like a pancakewhose parameters are shown here. If the volume of the drop is small, it will form a small drop whosecross section is a sphere. But that is not the worry of the housewife. The worry is a large puddle asshown here. Assume that 6 liters of water of density 1000 kg/m³ are spilled on the ground with contactangle θ_E . The surface tension is 0.49 N/m., g = 10m/s², atmospheric pressure is 10⁵ Pa.

Calculate the gauge pressure (in $N / m^{2}$ ) at the base of the puddle when the contact angle is $18 0^{\circ}$ .

TestHub · Accepted Answer

p = p 0 ​ + ρ g h ⇒ p g a ug e ​ = ρ g h h = ρ g 2 S ( 1 − c o s θ ) ​ For θ = 18 0 ∘ , we have ( 1 − cos θ ) = 2 . h = ρ g 4 S ​ = 1000 × 10 4 ( 0.49 ) ​ = 0.014 m p g a ug e ​ = ρ g h = 1000 × 10 × 0.014 = 140 N / m 2

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