Question

A bottom-mounted hole in the open tank allows an incompressible fluid to flow at a rate of 155 kg/s. The orifice's diameter is 6 mm. The liquid's density is 850 kg/m, Calculate the liquid level in the tank's height. Consider the coefficients of discharge and velocity (C d = 0.9). [Formula: vt = √2gh]

Answer 1

The liquid level in the tank can be found by calculating the cross-sectional area of the orifice, using the discharge rate to find the flow velocity, applying Torricelli's theorem, and correcting for the discharge coefficient.

Step-by-step explanation:

To calculate the liquid level in the tank's height, we first need to find the velocity of the fluid exiting through the orifice. The discharge rate (Q) of the fluid can be expressed as:

Q = Cd × A × v

Where:

• Cd is the discharge coefficient (0.9),
• A is the cross-sectional area of the orifice,
• v is the velocity of the fluid exiting the orifice.

The area (A) of the orifice can be calculated using the diameter (d = 6 mm) with the formula:

A = π × (d/2)²

Using the given flow rate (155 kg/s) and the liquid's density (ρ = 850 kg/m³), we can solve for the velocity (v).

Q = ρ × A × v ⇒
v = Q / (ρ × A)

Next, we use Torricelli's theorem, which states that the velocity (vt) of fluid flowing out of an orifice is:

vt = √(2gh), where g is the acceleration due to gravity and h is the height of the liquid level above the orifice.

By equating v to vt, and solving for h, we get:

h = (v/Cd)² / (2g)

After plugging in the values and solving, we can find the height of the liquid level in the tank.