6. THIS PROBLEM HAS THREE PARTS. THE FIRST Two, WITH THE SAME DIAGRAM SHOWN, ADD

Question

6. THIS PROBLEM HAS THREE PARTS. THE FIRST Two, WITH THE SAME DIAGRAM SHOWN, ADDRESS HYDROSTATICS. THE THIRD PART -(C) INVOLVES FLUID DYNAMICS AND A DIFFERENT SET UP WITHOUT A DIAGRAM. In a university geology lab, an ore sample - shown by white rectangle at bottom end of cord - weighs 19.50 N in air. When the sample is suspended by a light cord and totally immersed in water, the tension in the cord is T, 11.20 N. THE UPPER END OF CORD IS AT THE BLACK CEILING ATTACHMENT. (a) (25) Find the total volume of the sample. (b) (25) Find the density of the sample lab attic and ceiling earlier,later, T' = 11.20 N T 19.50 N lab floor (c) (10) At one point in a pipeline the water's speed is 5.00 m/s and the gauge pressure is 5.00x104 Pa. Find the gauge pressure at a second point in the line, 10.0 m lower than the first, if the pipe diameter at the second point is twice that at the first. Hint: Gauge pressure is absolute pressure minus atmospheric pressure. Make correct conversions at the proper points in the problem.

Explanation / Answer

In air

T - mg = 0

In water

T' - mg + Fb = 0

T - T' = Fb

Fb = buoyancy force = rho*V*g

T - T' = rho*V*g

19.5 - 11.2 = 1000*V*9.8

volume = 0.00085 m^3

========

part (b)

T = m*g = rho_sample*V*g

19.5 = rho_sample*0.00085*9.8

rho_sample = 2341 kg/m^3

================================

part(c)

from equation of continuity

volume flow rate remains same at all points

A1*v1 = A2*v2

A1 = pi*a1^2/4

A2 = pi*d2^2/4

d1 , d2 are diameters of pipe

d2 = 2d1

pi*d1^2/4*5 = pi*4*d1^2/4*v2

v2 = 1.25 m/s

from Bernoullis principle

P1 + (1/2)*rho*v1^2 + rho*g*h1 = P2 + (1/2)*rho*v2^2 + rho*g*h2

P2 = po + dP1

P1 = po + dP2

v2 = 1.25 m/s

v1 = 5 m/s

h1 = 10 m

h2 = 0

P2 = P1 + (1/2)*rho*(v1^2 - v2^2) + rho*g*(h1-h2)

Po + dP2 = po + 5*10^4 + (1/2)*1000*(5^2-1.25^2) + 1000*9.8*10

gauge pressure = dP2 = 1.59*10^5 Pa

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.