Question

A 6 cm steel pipe connects two reservoirs. The reservoirs are 50 m apart, the oilsurface in reservoir 1 is 15 m higher than in reservoir 2 , and reservoir 2 is a closed container with an internal pressure of 200kPa (gauge). If the fluid is SAE 30 oil, compute the flow rate.

Answer 1

To calculate the flow rate of the oil, we can use Bernoulli's equation, which relates the pressure difference and the resistance of the pipe. By finding the pressure difference between the two reservoirs and the resistance of the pipe, we can determine the flow rate.

Step-by-step explanation:

To calculate the flow rate of the oil through the 6 cm steel pipe, we can use the principle of Bernoulli's equation. The equation states that the pressure difference between the two reservoirs is equal to the difference in potential energy and the resistance of the pipe.

First, we need to find the pressure difference between the two reservoirs. The oil surface in reservoir 1 is 15 m higher, which means the potential energy difference is given by: ΔPE = mgh = density * volume * g * h.

Next, we need to calculate the resistance of the pipe using the viscosity of SAE 30 oil. The pressure difference is given by: ΔP = 32 * viscosity * L * flow rate / (pi * diameter^4).

Combining these equations, we can solve for the flow rate: flow rate = (density * g * h * pi * diameter^4) / (32 * viscosity * L).