Needle's tip - Problempedia

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Sergey_KuleshovSergey Kuleshov 3 weeks agoedited

If the needle is assumed to be hollow, then using this needle and a syringe with a known volume $V$ , one can estimate the size of the needle tip using drops. At the moment the drop separates from the needle tip, the force of gravity is balanced by the surface tension force:

m g = 2 π r σ,

where $r$ is the radius of the needle tip, $σ$ is the coefficient of surface tension of the liquid.
The mass of a drop can be estimated by slowly (drop by drop) emptying the syringe through this needle, counting the drops. Hence the mass of a drop can be calculated as:

m = ρ V / N,

where $ρ$ is the density of the liquid, $N$ is the total number of drops.
Hence the final formula for estimating the radius of the needle tip:

r = \frac{m g}{2 πσ} = \frac{ρ V g}{2 π N σ} .

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