A sphere of radius R=0.2 m is placed in incompressible irrotational flow with =10 m/s at sea level (The fluid has a density of ρ=1.2kg/m3 and pressure of 101325 pa). Calculate: The stagnation pressure at the top (θ=0∘) The pressure at the equator (θ=90∘) Compare both pressures to the free-stream dynamic pressure.

A sphere of radius R=0.2 m is placed in incompressible irrotational flow with =10 m/s at sea level (The fluid has a density of ρ=1.2kg/m3 and pressure of 101325 pa). Calculate: The stagnation pressure at the top (θ=0∘) The pressure at the equator (θ=90∘) Compare both pressures to the free-stream dynamic pressure.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. Figure for Part (a) U Figure for Part (b) 30 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p ) b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180° + 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then, calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )
The Question is attached as an image.
A tornado in atmospheric air is simulated by a CCW free vortex as a potential flow field. The velocity measured at r = 1 m from the center is 60 m/s. Determine the magnitude of dynamic pressure P at r = 10 m . (Use pi number = 3 , Air density = 1 .0 kg/m3 )ANSWER: P= 18 Pa
A circular cylinder is fitted with two surface-mounted pressuresensors, to measure pa at θ = 1808 and pb at θ = 105°.The intention is to use the cylinder as a stream velocimeter.Using inviscid theory, derive a formula for estimating U∞in terms of pa, pb, ρ, and the cylinder radius a.
Two radii rl and r2 (r2 > rl) in the same horizontal plane have the same values in a free vortex and in a forced vortex. The tangential velocity at radius rl is the same in both vortices. Determine, in terms of r1, the radius r2 at which the pressure difference between r1 and r2 in the forced vortex is twice that in the free vortex.
When a fluid originally at rest is accelerated on a streamline under steady flow conditions, Select all that apply. Select one or more: a. the hydrostatic pressure will increase b. the stagnation pressure will not change c. the total pressure will not change d. the stagnation pressure will decrease e. the static pressure will decrease
The velocity components for idealised flow along a right angled wall is given by u = 4 x m/s, v = -4 y m/s, w = 0 m/s. Find the vorticity magnitude at position x=(1,2,1) cm. Give your answer to two decimal places.
Problem 6.2 The gap between a moving plate of height H and a stationary wall is filled with an incompressible liquid with density pliq. The plate is pushed to the right at a constant speed Vplate. At the bottom sliding joint, there is a seal to prevent leakage. The gap width x and the liquid height y are continuously changing with time. The length dimension L into the page is constant. Side View: H V plate seal X Stationary wall (a) Determine rate of change of the liquid width with time, (d x/d t) in terms of the given variables (i.e., Vplate). (b) Assume the moving plate height H is tall enough that the liquid does not spill over. Determine the rising rate of the liquid top surface (d y/d t) in terms of the given variables. (c) Assume the moving plate height H is too short and the liquid spills over as the plate keeps moving. Determine the mass flow rate of the spillage in terms of the given variables.
This question is from course Fluid Mechanics. Kindly solve it.
Derive an expression for the capillary- height change h, as shown, for a fluid of surface tension Y and contact angle 0 be- tween two parallel plates W apart. Evaluate for water at 20°C if W = 0.5 mm.
The streamlines in a particular two-dimensional flow field are all concentric circles, as shown in Fig. 5 the equation v, = wr where w is the angular velocity of the rotating mass of fluid. Determine the circulation around the path ABCD. The velocity is given by B Figure 5
A piston moves with constant velocity U0 in a cylinder having radius R. A liquid having density leaves the open end with conical velocity proÖle V~ = V0(1-r/R)^k.Figure for problem 1.(a) If the exhaust port is closed, find the value of V0 in terms of U0. Be sure to define an appropriate control volume for solving this problem.(b) If V0 = U0, find the volume áow rate leaving through the exhaust port (in terms of U0 and R)