Question

Ethyl alcohol is in a 300 /- 10% mm-diameter tank at an initial height of 1 m. The ethyl alcohol exits the tank through an sharp-edged orifice, which has a diameter of 2 /- 10% mm and located at the bottom of the tank. The tank is open to the atmosphere. What is the approximate actual velocity along with propagation of uncertainty in m/s coming out of the orifice at ethyl alcohol height of 0.75 /- 10% m

Answer 1

The velocity of propagation is v = 3.836 m/s ±  5%

Data;

• diameter of tank = d = 300 ± 10 % mm
• initial height of tank H = 1m
• Exit tank diameter (Orifice) = d = 2 ± 10%

Velocity of Flow of Orifice

The velocity of the flow is calculated as

$v_h = \sqrt{2gh}$

h = height of the fluid from the orifice

h = 0.75 ± 10%m

$v = \sqrt{2*9.81*0.75}\\g = 9.81 m/s^2\\v = 3.836 m/s$

The uncertainty or error in calculating velocity

$v = \sqrt{2gh}$

The uncertainty = 1/2 * error in 'h'

$\frac{1}{2} * 10 \% = +5 \%$

The uncertainty = ± 5%

The velocity of propagation is v = 3.836 m/s ±  5%

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