d21.laurentian.ca + my Front Page - myLaurentian D2L Lab4_Instructions-PHYS1006E - Introductory Physics I - Lab Course Hero Q T V 1 of 5 + Automatic Zoom > > LAB 4 Fluid Dynamics 1. Purpose To demonstrate some fluid dynamic physics by using a bottle of water with a hole on the side of the bottle towards its bottom. The flow of water from the orifice will be photographed and image processing coupled with physics will allow measurements of water velocity at the orifice. 2. Theory Using the equation of energy conservation for a flow (Bernoulli's law), we can derive the velocity of the spout and validate the data. Let's compare the flow at two different points. Point 1 is at the surface of the water column inside the bottle, and point 2 is located exactly at the hole and a height of h below point 1 (Figure 1). point 1 h point 2d21.laurentian.ca + my Front Page - myLaurentian D2L Lab4_Instructions-PHYS1006E - Introductory Physics I - Lab Course Hero Q T V 1 of 5 + Automatic Zoom > > point 1 h point 2 Figure 1: Geometry of experiment and localization of points 1 and 2. Bernoulli's law can be written as: Pit pghi + - pv} = P2 + pgh2 + ; pv? Eq. 1 P is the pressure, p=1000 kg/m3 is the density of water, g=9.8 m/s2, h is the height, and v is the flow velocity. We arbitrarily set h2=0, and so h1=h is positive. Since the bottle drains very slowly we can approximate V1= 0. The pressure above the fluid column is P1= atmospheric pressure since the bottle is open to the atmosphere. The same is true for point P2 since PHYS 1006E-Lab 4 Instructions Page 1 of 5 imtool window to measure a given distance on the ruler in terms of the number of pixels. Then use this information to determine the size in mm of a pixel. (ii) Get the (x,y) pixel coordinates of the orifice. (iii) Choose a point on the parabolic trajectory and sing the orice location as the origin record its (x,y) pixel coordinates. (iv) Determine the (x,y) coordinates of the point determined in step (iii). (v) The x- and y-coordinates of points on the stream of water which is initially moving at v0 to the right (horizontally) are given by: x = vaAt 1 y = y(At)2 where g = 9.8 m/s2 and At is the time travelled to the given point. Solving for V0 gives x 170 = 2_y g PHYS 1006E-Lab 4 Instructions Page 4 of 5 d2l.laurentian.ca . F'nn: rage in} Leu'emia'i lE| LabA_lnstructions-PHVS'I006E - Introductory physics I - Lab which represents the velocity of the spout at the hole as a function of x and y. Calculate V0 5 times by using 5 different points on the spout. Calculate the mean value of V0 and the uncertainty of the mean. (vi) For each fill level photographed, obtain h and calculate the velocity V2 at the origin and its uncertainty. (vii) Fill in Table 1. Table 1: Give a descriptive caption. h : Ch 170 i 0170 V2i0'2 (cm) (cm/s) (cm/s) (viii) Plot V2 and 170 as a function of h. 5. Discussions (not more than a page) Question 2: Are the values V2 and 17,, consistent with each other? / A brief discussion of your observations. \\/ Give the possible sources of errors for this experiment. \\/ Provide ways to improve the experience. Marking Scheme Title Page 10 Points Answer the Question 1 in the introduction. 10 Points Provide a list of the materials used to conduct the experiment. Include uncertainties 5 Points V d21.laurentian.ca + Front Page - myLaurentian DEL Lab4_Instructions-PHYS1006E - Introductory Physics I - Lab Course Hero 5. Discussions (not more than a page) Question 2: Are the values v2 and v. consistent with each other? A brief discussion of your observations. Give the possible sources of errors for this experiment. Provide ways to improve the experience. Marking Scheme Title Page 10 Points Answer the Question 1 in the introduction. 10 Points Provide a list of the materials used to conduct the experiment. Include uncertainties 5 Points when applicable. Series of photographs of bottle with different fills levels and water spout. 15 Points One sample calculation of vo, and calculation of the mean of vo and its uncertainty. 15 Points One sample calculation of v2 and its uncertainty. 10 Points Table of v2 and v. as a function of fill level h. (Include associated uncertainties). 5 Points Graph of the mean of v and v2 as a function of h. 10 Points Discussions including the answer to Question 2. 10 Points Required footer*, neatness/clarity, uploaded to d21 as a single pdf file 10 Points TOTAL 100 Points *Required footer Last Name, First Name, student #, PHYS1006E-Lab 4 Page # of # pdf file name for the d21 dropbox LastName, FirstName-Student#-PHYS1006E-Lab4.pdf PHYS 1006E-Lab 4 Instructions Page 5 of 5 Download Print d2l.laurentian.ca |El Lab4_Template_PHY51006E - Introductory Physics I - Lab 4 or 3 1' HUIOmaIlC Loom V 1. Introduction: > Question 1 A large storage tank, open at the top and lled with water, develops a small hole in its side at a point 15.2 m below the water level. The rate of ow from the leak is found to be 2.80 x 10'3 m3 min". Refer to Figure 1. Figure 1 (a) Determine the speed (in m/s) at which the water leaves the hole. (b) Determine the diameter of the hole (in mm). (c) What If? If the hole is 10.0 m above the ground and the water is projected horizontally from the hole, how far (in m) from the base of the tank would a bucket have to be initially placed to catch the water from the leak? d2l.laurentian.ca |El Lab4_Template_PHY51006E - Introductory Physics I - Lab 1' HUIOmaIlC Loom v 2. Materials: 1 Provide a list of the materials used to conduct the experiment. Include the estimated uncertainties when applicable. / Provide a schematic diagram of your experimental setup. Last Name, First Name, student #, PHYSIOO6E-Lab 4 Page 2 of 3 3. Results \\/ Provide series of photographs of the bottle and spout for different ll levels. Include one photo of what happens with a cap on the bottle. / Show one sample calculation of v0. / Calculate V0 i Dvo- J Show one sgple calculation of v2 and its associated uncertainty > p26-31.gif a Offer Confirmed.eml Odale-Shatter_cone_formation.jpeg Details Ready Zoom: 100% UTF-8 CRLF script Ln 1 Col 1 NOW 22 A