Question

A tank is filled with water of density 1 g cm^-3 and oil of density 0.9 g cm³. The height of water layer is 100 cm and of the oil layer is 400 cm. If g = 980 cms^-2, then the velocity of efflux from an opening in the bottom of the tank is ______.

पर्याय

• `sqrt(900xx980)` cm s^-1

• `sqrt(1000xx980)` cm s^-1

• `sqrt(920xx980)` cm s^-1

• `sqrt(950xx980)` cm s^-1

Answer 1

A tank is filled with water of density 1 g cm^-3 and oil of density 0.9 g cm³. The height of water layer is 100 cm and of the oil layer is 400 cm. If g = 980 cms^-2, then the velocity of efflux from an opening in the bottom of the tank is `bbunderline(sqrt(920xx980)  "cm"  "s"^-1)`.

Explanation:

Pressure at the bottom of tank must equal pressure due to water of height h.

Let d_w​ and d_o​ be the densities of water and oil,

then the pressure at the bottom of the tank

= h_wd_wg + h₀d₀g

Let this pressure be equivalent to pressure due to water of height h. Then

hd_wg = h_wd_wg + h₀d₀g

∴ h = `"h"_"w"+("h"_0"d"_0)/("d"_"w")`

= 100 + 360 = 460 

According to Toricelli’s theorem,

v = `sqrt(2"gh")`

= `sqrt(2xx980xx460)`

= `sqrt(920xx980)` cm/s