Lab Report 2 Chem E

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Iowa State University *

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Mechanical Engineering

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Dec 6, 2023

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Armfield F1-17: Orifice and Free Jet Flow Abigale Houghtby, Rachel Bruggeman, Isaac Kamphaugh October 16 th ,2023 Abstract This experiment evaluated the coefficient of velocity and the discharge of an orifice within the lab and compared them with textbook values. The orifice and free jet flow apparatus contains a head cylindrical tank with an orifice plate attached into its side. The orifice plate discharges water using an adjustable overflow pipe, adjacent to the tank, which allows those to change the water level. The hose attached to the overflow pipe allows excess water to return to the hydraulic bench. Further experiments should be conducted with a larger orifice plate, possibly allowing flow rate to be more accurate rather than using one too small that may allow for more error within an experiment.

Introduction An orifice is the opening in a pipe or the side of a wall of a container (reservoir or a water tank), which the fluid can discharge from the reservoir. The orifice can be used to measure the flow rates if the geometric properties of the orifice and when the inherent properties of the liquid are known. The flow measurements of an orifice are based off the application of Bernoulli’s equation, stating that a relationship can only exist between the pressure of a fluid and the liquid’s velocity. The flow velocity and discharge can be calculated based on the Bernoulli’s equation, which should be corrected to include the viscosity and the effects of energy loss. As a result, to get the most accurate results, the coefficient of velocity and the coefficient of discharge should be calculated for the orifice within the experiment. The goal of this experiment is to conduct a balance of the coefficients of the orifice. Theory The orifice outflow of the velocity can be calculated by using Bernoulli’s equations for a frictionless, steady flow to the reservoir with the orifice opening on its side. The following equation was used: V i = √ 2 g∆ H In the equation above, H represents the height of the fluid above the orifice. The ideal velocity is the height of the fluid because the effect of fluid viscosity is not contemplated in deriving Equation 1. The actual flow of velocity is smaller than V i and can be calculated as: V = Cv √ 2 g∆ H In the equation above, C v represents the coefficient of velocity, allowing for viscosities effects, C v <1. The actual outflow can be calculated by equation 2 at the velocity at the vena contracta, where the velocity flow is at its maximum and its diameter is at its minimum. In order to find its actual flow rate, use the following equation: Q = vAc In the equation above, A c is the vena contracta’ s flow area. A c is much smaller than the orifice area, A o , and is given by the following equation: Ac = CcAo In the equation above, C c is represented as the coefficient of contraction; consequently C c <1. From the variables of V and A c from equations 2 and 4, substitute those into equation 3, resulting in the following equation: Q = CdAo √ 2 gh In the equation above, the velocity, C v , and the discharge of coefficient, C d , are both determined by the experiment. Methods

The method of this experiment is the coefficients of the velocity and discharge, which is determined by measuring with the equipped needles, the trajectory of the jet projecting water from an orifice on the side of the reservoir under a steady flow condition. Results and Discussion Table 1: The below table (Table 1) contains the data that had been gathered from the various trials as well as the fluid head measurements. Diameter of the Orifice: 3 mm Trial Fluid Head 1 369 mm 2 350 mm 3 330 mm 4 310 mm 5 290 mm 6 268 mm Table 2: The below table (Table 2) contains the data that had been gathered from the various trials as well as the x and y values. Gathering the flow rates of each y value. Trials (x) Y (268) Y (290) Y (310) Y (330) Y (350) Y (369) 50 0 0 0 0 0 0 100 0.7 0.7 0.5 0.6 0.5 0.45 150 2.1 2.1 2.8 1.5 1.50 1.45 200 3.7 3.7 3.3 0.3 3.00 2.90 250 6.1 6.0 5.0 4.8 5.00 4.60 300 8.6 8.6 7.4 6.8 6.90 6.70 350 11.7 11.8 10.0 9.5 9.30 9.00 400 15.3 15.5 13.4 12.6 12.5 11.80 After identifying the x and y values, a plot can be made to evaluate the flow rate from each fluid head (Graph 2).

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0 50 100 150 200 250 300 350 400 450 0 5 10 15 20 Fluid Rate vs Fluid Head Y (268) Y (290) Y (310) Y (330) Y (350) Y (369) Fluid Head Fluid Rate Conclusion From this experiment it was found that the orifice coefficient of velocity and the discharge of an orifice within the lab can compare to those values within a textbook or reliable sources. The findings of this experiment have been determined that the flowrate affects the coefficient of water discharge, the lower the flow rate may be means the higher the coefficient of water discharge and the higher the flow rate may be means the lower the coefficient of water discharge. The flow rate is proportional to the square root pressure, allowing the given orifice to be equal to its constant.